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Natural Language Actor-Critic: Scalable Off-Policy Learning in Language Space (2512.04601v1)

Published 4 Dec 2025 in cs.LG and cs.CL

Abstract: LLM agents -- LLMs that dynamically interact with an environment over long horizons -- have become an increasingly important area of research, enabling automation in complex tasks involving tool-use, web browsing, and dialogue with people. In the absence of expert demonstrations, training LLM agents has relied on policy gradient methods that optimize LLM policies with respect to an (often sparse) reward function. However, in long-horizon tasks with sparse rewards, learning from trajectory-level rewards can be noisy, leading to training that is unstable and has high sample complexity. Furthermore, policy improvement hinges on discovering better actions through exploration, which can be difficult when actions lie in natural language space. In this paper, we propose Natural Language Actor-Critic (NLAC), a novel actor-critic algorithm that trains LLM policies using a generative LLM critic that produces natural language rather than scalar values. This approach leverages the inherent strengths of LLMs to provide a richer and more actionable training signal; particularly, in tasks with large, open-ended action spaces, natural language explanations for why an action is suboptimal can be immensely useful for LLM policies to reason how to improve their actions, without relying on random exploration. Furthermore, our approach can be trained off-policy without policy gradients, offering a more data-efficient and stable alternative to existing on-policy methods. We present results on a mixture of reasoning, web browsing, and tool-use with dialogue tasks, demonstrating that NLAC shows promise in outperforming existing training approaches and offers a more scalable and stable training paradigm for LLM agents.

Summary

  • The paper introduces a novel Natural Language Actor-Critic framework that replaces scalar rewards with generative textual critiques to enhance policy refinement.
  • It employs a language-based Bellman backup and off-policy training strategy, achieving significant sample efficiency and up to 25% task performance improvement.
  • Empirical results show NLAC outperforms traditional RL methods in multi-turn dialogues and strategic tasks by providing actionable, language-grounded feedback.

Natural Language Actor-Critic: Scalable Off-Policy Learning in Language Space

Introduction and Motivation

The "Natural Language Actor-Critic" (NLAC) framework advances the training paradigm for LLM agents, specifically targeting multi-turn, long-horizon agentic tasks operating in structured environments. The core motivation is to transcend the limitations of current LLM policy optimization schemes, which predominantly rely on on-policy policy-gradient methods (PPO, GRPO) and scalar reward signals. Such methods exhibit high sample complexity, instability, and poor credit assignment, particularly under sparse, delayed-reward conditions and in combinatorially large natural language action spaces. Unlike prior RL-for-language approaches, NLAC redefines the actor-critic framework by introducing a generative LLM critic that outputs textual evaluations rather than scalar values, enabling LLMs to leverage their reasoning capabilities for improved policy refinement and sample efficiency (2512.04601).

Methodological Innovations

The key novelty of NLAC lies in reformulating policy evaluation and improvement around natural language—rather than real-valued—feedback. The approach comprises:

  • Language-Space Critic Learning: NLAC trains a generative LLM critic to produce textual critiques QLπ(s,a)∈V∗Q_L^\pi(s, a) \in \mathcal{V}^*, which explain both the outcome and justification for each action. This is operationalized as supervised learning of a language successor model via a bespoke language Bellman backup—an analogue of distributional RL, but in text space. The backup defines an iterative process whereby next-state, reward, and recursively generated future rollout descriptions are composed to produce a distribution over possible trajectory narratives.
  • Policy Refinement by Critique: Rather than pursuing direct argmax extraction over the (intractably huge) language action space, NLAC employs an iterative self-refinement strategy. The LLM policy proposes an action, receives a textual critique from the critic, and subsequently conditions on this critique to generate a refined action. Empirically, a single round of refinement yields substantial improvements, but the mechanism is structurally designed for multi-step refinement.
  • Scalable Off-Policy Training: Both policy and critic training leverage off-policy data, using prioritized experience replay and cross-entropy objectives. Since the language Bellman backup and refinement steps do not require on-policy rollouts, NLAC is considerably more sample-efficient than standard RL fine-tuning approaches.

Theoretical Properties

NLAC is theoretically characterized by a connection to successor features. Under linear reward assumptions and assuming the language Bellman backup corresponds to discounted feature sum aggregation under the LLM's encoding, the paper proves:

  • Consistency: The text-based QLπQ_L^\pi can be mapped monotonically to the true scalar QπQ^\pi, allowing for correct policy improvement in expectation.
  • Convergence: Iterative application of language-based policy evaluation and improvement converges to a policy that is at least as good as any other policy in the environment.

This analysis critically bridges the representational gap between language-generation and scalar value function RL literature, ensuring the practical viability of NLAC.

Empirical Results

NLAC was benchmarked against prompting baselines (GPT-4.1 with ReAct), rejection/refinement fine-tuning, on-policy RL baselines (PPO, GRPO), and ablations (scalar SAC, Natural Language RL with enumeration [NLRL]). The evaluation covers: mathematical reasoning (MATH-Hard), strategic multi-turn dialogue (20Q), and tool-augmented customer service dialogues (τ\tau-Bench).

Notable results:

  • On 20Q, NLAC attains a 32.1% winrate with QwQ-32B, outperforming all RL finetuning approaches and matching or exceeding powerful prompting-based methods (e.g., GPT-4.1 ReAct).
  • On τ\tau-Bench retail, NLAC achieves 0.59 task completion, a 25%+ improvement over PPO/GRPO and NLRL, and the only method robust on generalization to unseen airline domain scenarios.
  • On single-turn MATH, NLAC and NLRL perform similarly, indicating the specificity of NLAC's advantage to multi-step problems.

Ablations show that naively learning Q-values in scalar or sampled token spaces is ineffective for sequence-level language agent tasks—NLRL, which requires enumeration and context-window aggregation, is found both intractable and less effective than NLAC's bootstrapped, off-policy text-based Bellman learning.

Qualitative analyses indicate that NLAC's language critic frequently identifies nuanced failure modes in multi-turn interactions and delivers actionable critiques that drive policy correction in scenarios where scalar reward signals are insufficient for effective exploration or credit assignment.

Practical and Theoretical Implications

NLAC represents a paradigm shift for aligning LLM agents in complex environments, with multiple implications:

  • Practical: By providing rich, actionable feedback, NLAC enables LLM agents to explore and improve via targeted self-refinement, sidestepping the inefficiencies of undirected exploration. This is critical for tasks with multipart goals and domain constraints (e.g., customer service, tool-based dialog, open-ended games).
  • Theoretical: The approach links language generation, distributional RL, successor features, and policy iteration, revealing a plausible pathway for integrating complex reasoning into RL policy improvement in arbitrarily large language spaces.
  • Generalization and Alignment: The critic's textual outputs serve not only as an evaluation metric but a form of process supervision; this could serve as a foundation for richer, process-based alignment strategies in agentic LLMs.

Potential future extensions include leveraging learned natural language critics to train scalar reward models for classical RL/IL pipelines, or integrating NLAC with return-conditioned sequence modeling approaches (e.g., Decision Transformers).

Conclusion

NLAC demonstrates that textual, language-grounded feedback enables both scalable off-policy learning and improved sample efficiency for LLM-based agents in complex, long-horizon environments. The framework is theoretically principled, empirically validated across diverse agentic domains, and highlights the dual role of language as both action space and rich policy improvement signal. NLAC is likely to influence agentic LLM alignment both as a practical recipe and a conceptual foundation for process-supervised, language-native agent learning (2512.04601).

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Overview

This paper introduces a new way to train LLM agents—computer programs that use language to act step by step in the world, like asking questions in a game, browsing the web, or helping a customer. The method is called Natural Language Actor-Critic (NLAC). Instead of judging actions with a single number (like a score), NLAC trains a “critic” that writes text feedback explaining what was good or bad about an action and how to improve it. This makes learning more stable and efficient, especially for long tasks where rewards are rare and actions are open‑ended (anything you can say in language).

Key Objectives

The paper aims to answer simple, practical questions:

  • How can we train LLM agents to do multi-step tasks when there aren’t many examples of experts doing them?
  • Can we replace fragile “number-only” feedback with helpful written feedback that LLMs can understand and use?
  • Can we train efficiently using past experiences (“off-policy”) instead of constantly collecting new data?

How It Works (Methods)

The “Actor” and the “Critic”

Think of training an agent like training an athlete with a coach:

  • The actor is the agent—the part that decides what to do next (what to say, what tool to call, etc.).
  • The critic is the coach—the part that evaluates those actions and explains why they were good or bad.

Traditional methods give the actor only a single number (the score) as feedback. NLAC’s critic instead writes natural language explanations. This fits LLMs better, because they already understand and reason in text.

Predicting the Future in Words

To give useful feedback, the critic needs to predict what might happen next. NLAC teaches the critic to be a “future storyteller”:

  • Language successor model: Imagine a fortune teller who describes what is likely to happen after a given action—short summaries of possible future steps and outcomes.
  • Language Bellman backup: A training trick that builds these future stories one step at a time. It merges “what happens immediately next” with “what likely happens later” into a single, coherent written description. You can think of it like writing a chapter: first the next scene, then a short outline of later events, combined into a readable summary.

Because this process uses one-step updates from stored past experiences, it can be trained off-policy—meaning the model doesn’t need to constantly generate new data to learn, which saves time and makes training more stable.

Training Without Constant New Play (“Off-Policy”)

Many RL methods require the agent to keep playing and collecting fresh trajectories with the current policy at every step (“on-policy”). That’s slow and unstable. NLAC learns from a replay buffer—a memory of past interactions—so it can train even when not actively playing. This reduces the number of samples needed and avoids large, risky updates.

Improving Actions by Self-Refinement

The critic’s written feedback doesn’t just say “good” or “bad”—it explains why and suggests how to fix mistakes. NLAC uses this to refine actions:

  • Refinement policy: The actor proposes an action. The critic writes a short explanation of what might go wrong or how to improve it. The actor then revises its action based on that feedback.
  • Distillation: Over time, the actor is trained (like copying from a better version of itself) to produce these refined actions directly, without needing multiple attempts.

This avoids trying every possible action (impossible in language, where there are countless options) and replaces random exploration with guided self-correction.

Main Findings

The authors test NLAC on three types of tasks:

  • Math problem solving (MATH): single-step reasoning problems.
  • 20 Questions (20Q): a multi-turn dialogue game where the agent guesses a hidden object by asking questions.
  • Customer service with tools (τ‑Bench): multi-step tasks mixing conversation and tool calls, following strict guidelines.

What they observed:

  • On long-horizon tasks (20Q and τ‑Bench), NLAC beat popular training methods like PPO and GRPO, and even outperformed zero-shot prompting from a very strong model in many cases.
  • NLAC learned faster and more stably, needing fewer training steps to reach top performance.
  • On single-step math, NLAC performed similarly to strong baselines (since there’s less “future” to predict, text feedback reduces to explaining the final reward), but its main advantages showed up in multi-step tasks.

They also provide theory showing that, under reasonable assumptions, their method leads to consistent improvement and can reach the optimal policy. In plain terms: if the critic’s internal representations correctly summarize what’s likely to happen and why, then using those summaries to guide refinements will steadily make the agent better.

Why It Matters

  • More helpful feedback: Instead of just “+1” or “0,” the agent gets a readable explanation of what went wrong and how to fix it. That’s exactly the kind of feedback LLMs can use well.
  • Better for complex, open-ended actions: When “actions” are sentences or tool calls, brute-force exploration is hard. NLAC turns feedback into guidance, making it easier to discover smarter strategies.
  • More stable and efficient training: Off-policy learning from past experiences reduces the need for constant data collection and makes training less noisy.
  • Practical impact: Stronger LLM agents can handle complicated tasks—like web browsing, multi-step customer support, or planning with tools—more reliably. This could improve real-world systems that need careful reasoning and rule-following over many steps.

In short, NLAC teaches LLM agents using language, not just numbers—helping them learn faster and perform better on the kinds of multi-step tasks where language and reasoning really matter.

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Knowledge Gaps

Knowledge gaps, limitations, and open questions

Below is a single, consolidated list of concrete gaps and unresolved questions that the paper leaves open, intended to guide future research:

  • Validity of core theoretical assumptions:
    • The reward linearity assumption r(s,a)=ϕ(s)⋅wr(s,a)=\phi(s)\cdot w ignores action-dependent effects beyond state features; how to relax or replace this with more realistic function classes while preserving tractable analysis?
    • The assumption that the language Bellman backup corresponds to a discounted sum in representation space (Assumption 3) lacks empirical verification; can we measure whether learned representations behave like successor features in practice?
    • The assumption that textual critiques induce a total order over actions requires a reliable sentiment-to-return mapping; how well does this ordering correlate with true returns across tasks?
  • Convergence guarantees vs practice:
    • Theorems rely on a refinement “oracle” that always proposes non-worse actions; in practice, refinement is prompt-based and fallible. What convergence or monotonic improvement guarantees hold under realistic, noisy refinement?
    • How sensitive is convergence to errors in the successor model and evaluator, and do errors accumulate under repeated bootstrapping?
  • Calibration and faithfulness of textual critics:
    • How to quantitatively verify that generated critiques are faithful (evidence-based) and calibrated with respect to true value differences, rather than post-hoc rationalizations?
    • Can we derive or learn a monotonic mapping g from text to scalar value that reliably tracks returns across domains?
  • Language Bellman backup design:
    • The backup function B (“discounting” and combining immediate effects with future descriptions) is under-specified; which concrete designs best reduce compounding error and preserve temporal credit assignment?
    • Choice of divergence in Eq. (1) is not analyzed; how do different f-divergences (e.g., forward/reverse KL, JS, Wasserstein) affect stability, diversity, and sample efficiency?
  • Off-policy learning rigor:
    • The successor model conditions on policy-induced futures without sampling at+1∼πa_{t+1}\sim\pi; how large is the distribution mismatch as the policy changes, and can importance weighting or conservative objectives mitigate it?
    • What are the failure modes when training purely off-policy from replay buffers with stale data, and how can we detect and correct them?
  • Exploration and coverage:
    • The method claims reduced reliance on random exploration but provides no exploration guarantees or metrics; how to incorporate and measure explicit uncertainty, novelty bonuses, or posterior sampling in language space?
    • Can the critic/predictor quantify epistemic uncertainty over futures (e.g., via ensembles or Bayesian decoding) to guide more informative refinement?
  • Refinement process characterization:
    • Only a single refinement round (m=1m=1) is used; what is the trade-off curve for m>1 in performance vs compute/latency, and when do diminishing returns or instabilities appear?
    • How to handle incorrect or conflicting critiques (refinement in the wrong direction), and can we detect when to ignore or downweight a critique?
  • Component training strategy:
    • The evaluator E and refinement policy are largely prompt-based; would training them (e.g., via preference data, pairwise ranking, or PRM-like objectives) yield better alignment and performance?
    • What is the impact of sharing the same LLM parameters across policy, successor model, evaluator, and refinement modules (interference, bias, and self-confirmation)? Would separate or partially shared models perform better?
  • Scalability and compute:
    • Generating futures and critiques per step is costly; what are the training/inference-time compute and memory profiles vs PPO/GRPO, and how can we amortize or cache predictions without degrading performance?
    • Context window limits force summarization of multiple futures; how do longer horizons affect summary fidelity, and can hierarchical/structured summaries mitigate context overflow?
  • Stability and catastrophic forgetting:
    • The method notes susceptibility to forgetting and relies on “low-data regimes”; which regularization techniques (e.g., LwF, replay mixing, elastic weight consolidation) are most effective for NLAC?
    • EMA targets and reverse KL are used to prevent generative collapse; what is their sensitivity and are there better stabilization mechanisms?
  • Empirical validation gaps:
    • No systematic evaluation of the correlation between critique sentiment and true returns; can we establish rank correlation (e.g., Kendall’s τ) between QLπQ_L^\pi-induced ordering and ground-truth returns?
    • Lack of sensitivity analyses for key hyperparameters (k, m, λ1/λ2, replay prioritization α, EMA τ); what are robust defaults and operational ranges?
    • No ablation on k>1 (number of futures sampled) for stochastic tasks; how does k impact performance, calibration, and compute?
  • Benchmarks and generalization:
    • Experiments omit real web-browsing or more complex tool-use domains despite claims; how does NLAC fare on irreversible, partially observable, or highly stochastic environments?
    • Cross-domain generalization is tested only from retail to airline in τ-bench; broader evaluations with multiple unseen domains and harder shifts are needed.
    • The use of GPT-4.1 as judge/oracle may introduce bias; how robust are results to different evaluators and to noisy or adversarial feedback?
  • Baseline coverage and fairness:
    • The SAC ablation uses token-level Q-functions; would action-level or sequence-level Q-learning baselines (e.g., Q-Transformer variants) narrow the gap?
    • NLRL comparisons are compute- and design-constrained (e.g., limiting enumerations to 8); more controlled compute-matched studies are needed to ensure fairness.
    • Missing comparisons to PRM-based stepwise reward shaping, off-policy preference-based methods, and recent off-policy language RL methods.
  • Safety, robustness, and ethics:
    • The approach may produce confident but incorrect rationales (hallucinated critiques) that mislead refinement; how to detect and penalize unfaithful explanations?
    • No analysis of adversarial prompts, reward hacking against judges, privacy concerns in logged dialogues, or safety in tool-use.
  • Practical deployment considerations:
    • In latency-critical settings, iterative refinement within a step may be infeasible; what are strategies for budgeted refinement or one-shot policies distilled from NLAC?
    • How to integrate NLAC with real-time tool APIs where partial actions are irreversible and refinement cannot “overwrite” decisions?
  • Representation learning diagnostics:
    • The paper posits a connection to successor features but provides no empirical probes; can we directly measure whether learned representations approximate SFs and whether this predicts downstream performance?
  • Data usage and offline RL:
    • Can NLAC leverage large offline logs (e.g., customer support transcripts) safely and effectively? What forms of conservative or pessimistic objectives are needed to avoid overestimation from model-generated futures?
  • Decoding and control knobs:
    • The impact of decoding strategies (temperature, nucleus sampling) on successor diversity, critique reliability, and policy refinement is unexplored; what settings optimize stability vs exploration?
  • Remaining failure modes:
    • What systematic errors persist (e.g., over-general plans, rule misinterpretation, premature tool calls), and can targeted critique templates or structured feedback reduce them?
  • Reproducibility and transparency:
    • Details on compute budgets, wall-clock time, and exact prompts are relegated to appendices; standardized reporting and open resources would aid independent verification.
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Glossary

  • actor-critic: A reinforcement learning paradigm where a policy (actor) and a value estimator (critic) are learned jointly, with the critic guiding policy improvement. "In this work, we propose a new actor-critic algorithm \citep{haarnoja2018soft} to train LLM agents, where a critic (which estimates the value of actions) is jointly learned with a policy, both using off-policy data."
  • Bellman backup: The recursive update that enforces consistency of value estimates by bootstrapping from next-step values. "Such Q-functions are learned by regressing to their Bellman backup:"
  • catastrophic forgetting: The tendency of neural models to lose previously learned capabilities when fine-tuned on new tasks without care. "Like other methods that utilize pretrained LLMs, our method is susceptible to catastrophic forgetting."
  • chain-of-thought prompting: A prompting technique that encourages models to articulate intermediate reasoning steps to improve problem solving. "One of the greatest advantages of doing so is the ability to leverage the strong reasoning capabilities of LLMs from chain-of-thought prompting \cite{wei2023chainofthought, yao2022react}."
  • credit assignment: Determining which actions in a long trajectory contributed positively or negatively to the final outcome. "This makes credit assignment, or distinguishing between good and bad actions in a long rollout, difficult."
  • distributional Bellman backup: A variant of the Bellman update that learns the full distribution of returns instead of just their expectation. "which introduces a distributional Bellman backup to train a distribution over returns rather than just their scalar expectation."
  • distributional value learning: Learning value distributions over returns rather than scalar expectations to capture uncertainty and variability. "we draw inspiration from distributional value learning~\citep{bellemare2017distributional}, which introduces a distributional Bellman backup to train a distribution over returns rather than just their scalar expectation."
  • generative collapse: A failure mode in generative training where a model’s outputs degenerate, often due to self-conditioning or feedback loops. "where θˉ\bar{\theta} are reference parameters that are an exponentially moving average of the trained parameters, in order to prevent generative collapse ~\citep{Shumailov2024AIMC}."
  • Group Relative Policy Optimization (GRPO): A policy gradient variant that uses group-based relative rewards to stabilize optimization. "the prevailing training methods focus on policy optimization using algorithms such as Proximal Policy Optimization (PPO) ~\citep{schulman2017proximal} or Group Relative Policy Optimization (GRPO) \citep{shao2024deepseekmathpushinglimitsmathematical}."
  • KL-divergence: A measure of divergence between probability distributions, often used as a training objective or regularizer. "We choose the reverse direction of KL-divergence to capture the full diversity over possible futures."
  • language Bellman backup: A Bellman-style update defined over distributions of textual future descriptions instead of scalar values. "we propose a language Bellman backup BL\mathcal{B}_L that bears some semblance to the distributional Bellman backup, but makes key adaptations to account for samples that are textual descriptions of rollouts rather than scalar returns."
  • language evaluator: A component that aggregates predicted textual futures to produce a natural-language critique of an action’s quality. "A language evaluator EE takes as input state sts_t and action ata_t, along with a sequence of descriptions of possible rollouts (s,a)t+1:T(s, a)_{t+1: T} and their rewards r(sT)r(s_T), and outputs a textual critique that comments on whether ata_t was optimal, with justification using possible future outcomes."
  • language successor model: A model that probabilistically generates textual descriptions of future rollouts and outcomes conditioned on the current state-action. "A language successor model MπM^\pi for policy π\pi takes a state sts_t and action ata_t as input, and probabilistically generates a textual description of rollout (s,a)t+1:T(s, a)_{t+1: T}, or what will happen to policy π\pi in the future, and reward r(sT)r(s_T)."
  • LLM agent: An LLM configured to interact with environments over multiple steps, taking actions and receiving observations. "LLM agents---LLMs that dynamically interact with an environment over long horizons---have become an increasingly important area of research, enabling automation in complex tasks involving tool-use, web browsing, and dialogue with people."
  • Markov decision process (MDP): A formal framework for sequential decision-making defined by states, actions, transitions, rewards, and a discount factor. "We adopt the formalism of a Markov decision process (MDP) given by M=(,,P,r,ρ,γ)M = (, , P, r, \rho, \gamma)"
  • maximum-entropy optimization: Policy extraction that prefers higher-entropy (more exploratory) policies consistent with learned values. "Then, an improved policy π′\pi' can be derived using the Q-function via greedy or maximum-entropy optimization $\pi'(a_t | s_t) \propto \exp(Q\pi(s_t, a_t))."
  • Monte-Carlo rollouts: Trajectories sampled to estimate returns without bootstrapping, often used for baseline or training signals. "the difference being that PPO additionally learns a token-level value function on Monte-Carlo rollouts as a baseline to stabilize reward"
  • Natural Language Actor-Critic (NLAC): The proposed algorithm that trains policies using a critic that produces natural-language evaluations and enables off-policy refinement. "In this paper, we propose Natural Language Actor-Critic (NLAC), a novel algorithm for training LLM agents, where a natural language critic is jointly trained with a policy, and its evaluations directly inform how to perform policy improvement."
  • Natural Language Reinforcement Learning (NLRL): A framework that learns policies and critics in language space via in-context aggregation and enumeration. "Notably, \citet{feng2025naturallanguagereinforcementlearning} propose Natural Language Reinforcement Learning (NLRL) as a framework for learning policies and critics in language space."
  • off-policy: Training that uses data generated by policies other than the current one, often from a replay buffer. "our approach can be trained off-policy without policy gradients"
  • on-policy: Training that relies exclusively on trajectories sampled from the current policy. "First, these algorithms are notoriously data-inefficient because they are on-policy, meaning they require sampling new trajectories from the current policy at every training step."
  • policy evaluation: The step of estimating how good actions are under a policy, typically via a critic. "where each step consists of (1) policy evaluation, where a critic is trained to assess actions by a policy"
  • policy gradient methods: Algorithms that optimize policies directly via gradients of expected returns. "training LLM agents has relied on policy gradient methods that optimize LLM policies with respect to an (often sparse) reward function."
  • policy improvement: Updating the policy to take better actions based on evaluations or value estimates. "and (2) policy improvement, where the policy is updated using evaluations by the critic"
  • policy iteration: Alternating rounds of policy evaluation and policy improvement to converge to an optimal policy. "Our work aims to address key limitations in NLRL to make policy iteration in language space scalable to all LLM agent tasks."
  • prioritized replay buffer: A replay mechanism that samples transitions with probabilities proportional to a priority signal, e.g., loss. "In practice, we found it helpful to implement D\mathcal{D} as a prioritized replay buffer weighted by L1(st,at,st+1)\mathcal{L}_1(s_t, a_t, s_{t+1}) with sampling parameter α\alpha \citep{schaul2016prioritizedexperiencereplay}."
  • Proximal Policy Optimization (PPO): A popular on-policy algorithm that constrains policy updates via clipping to improve stability. "the prevailing training methods focus on policy optimization using algorithms such as Proximal Policy Optimization (PPO) ~\citep{schulman2017proximal} or Group Relative Policy Optimization (GRPO) \citep{shao2024deepseekmathpushinglimitsmathematical}."
  • process reward model (PRM): A model that provides intermediate, step-level feedback rather than only final trajectory-level rewards. "Process reward models (PRMs) aim to address this, particularly by providing action-level feedback using either human annotations ~\citep{lightman2023letsverifystepstep}, or an estimated value function in the absence of human intervention~\citep{wang2024mathshepherdverifyreinforcellms,setlur2024rewardingprogressscalingautomated}."
  • Q-function: The state-action value function that estimates expected return from taking an action in a state under a policy. "Actor-critic algorithms additionally learn a state-action value function, or Q-function, defined as Qπ(st,at)=E(s,a)t+1:∞∼pπ∑t′=tT−1γt′−tr(st′,at′)Q^\pi(s_t, a_t) = E{(s, a)_{t+1:\infty} \sim p^\pi}{\sum_{t' = t}^{T-1}\gamma^{t' - t} r(s_{t'}, a_{t'})}."
  • ReAct prompting: A prompting pattern that combines explicit reasoning (“thought”) with subsequent environment actions. "ReAct prompting is a popular method to leverage chain-of-thought reasoning of LLMs for long-horizon planning, by instructing LLMs to explicitly articulate their high-level plans \citep{yao2022react}."
  • refinement policy: A policy that revises an initial action using the critic’s textual feedback to produce a better action. "we define a refinement policy πr\pi^r that takes an action at∼π(⋅∣st)a_t \sim \pi(\cdot|s_t) by the base policy, and generates a refined action atr∼πr(⋅∣st,at,QLπ(st,at))a^{r}_t \sim \pi^r(\cdot|s_t, a_t, Q^\pi_L(s_t, a_t)) that is better according to the natural language critic"
  • soft actor-critic (SAC): An off-policy actor-critic method that optimizes a maximum-entropy objective for robustness and exploration. "We consider an ablation of our approach that is soft actor-critic (SAC) training."
  • successor features: A representation that captures expected discounted future feature occupancy under a policy, enabling efficient value computation. "Theoretically, we are able to connect the learned representations of our critic to successor features \citep{barreto2018successorfeaturestransferreinforcement}, allowing us to prove convergence to the optimal policy."
  • temporal-difference learning: A class of methods that learn by bootstrapping from successive predictions rather than waiting for full returns. "Note that our training objective is an instance of temporal-difference learning and thus does not require on-policy Monte Carlo trajectories."
  • token-level value function: A value estimator defined at the granularity of individual generated tokens to stabilize sequence-level training. "the difference being that PPO additionally learns a token-level value function on Monte-Carlo rollouts as a baseline to stabilize reward"
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Practical Applications

Immediate Applications

The following applications can be deployed now using NLAC with current LLMs, existing logs/datasets, and standard tool integrations. Each item notes relevant sectors, likely tools/workflows, and key assumptions or dependencies.

  • Customer service agents with tool-use and policy compliance
    • Sectors: retail, airlines, telecom, utilities, e-commerce
    • What to build: NLAC-trained agents that execute API calls (modify orders, exchanges, reservations) while adhering to scripted guidelines; “Critic-as-a-Guardrail” module that flags and explains policy violations at action time; dashboards that surface textual critiques to supervisors
    • Workflow: construct a replay buffer from historical chat logs and tool-call traces; train the language successor model via the language Bellman backup on off-policy data; run action refinement loops at inference to preempt violations (e.g., consolidate multiple exchanges into a single compliant tool call)
    • Assumptions/dependencies: access to high-quality logs and reward heuristics (task completion, adherence to policies); reliable tool APIs; privacy/compliance (PII handling); base LLM must be capable of multi-step tool-use; mapping textual critiques to a scalar “sentiment” for ordering
  • Strategic dialog assistants that ask better questions (discovery, diagnostics)
    • Sectors: sales, customer discovery, technical support triage, education (Socratic tutoring)
    • What to build: chatbots that optimize information gain (e.g., avoiding linear search over irrelevant attributes); an “Ask-Next” planner informed by the critic’s rollouts
    • Workflow: off-policy training on Q&A logs; critic-generated rationales that highlight discriminative features to query next; single-step refinement to improve questioning strategy
    • Assumptions/dependencies: measurable success signals (e.g., accurate identification within bounded turns); reliable automatic judges or human labels for task success
  • Web research and browsing agents
    • Sectors: knowledge work, market research, compliance research
    • What to build: “DeepResearch++” agents that minimize random exploration by using critic-proposed futures; textual critiques guide query reformulation and source selection
    • Workflow: collect browsing logs; define reward proxies (answer accuracy, citation quality); off-policy training of successor model; refinement-in-the-loop at inference
    • Assumptions/dependencies: tool integrations (search, scraping, RAG); robust reward modeling for research quality; guardrails against hallucination
  • Educational tutors for step-by-step problem-solving
    • Sectors: education, test prep
    • What to build: math and logic tutors that self-refine solution steps using critic feedback; step-level textual feedback to learners (“process rewards”) rather than only final correctness
    • Workflow: use existing datasets (e.g., MATH) with solution traces; train critic to predict and explain future outcomes for alternative steps; deploy refinement to improve hint quality
    • Assumptions/dependencies: curated curricular datasets; alignment to pedagogy; base LLM reasoning strength; evaluation beyond single-step accuracy
  • Software engineering assistants for multi-step tasks
    • Sectors: software, DevOps
    • What to build: IDE plugins and code assistants that explain why an action (e.g., test selection, issue triage, PR review) is suboptimal; refinement suggestions that reduce wasted exploration
    • Workflow: replay buffer from issue trackers, CI logs, PR discussions; successor modeling of downstream outcomes (test failures, code review responses); action refinement to propose better next steps
    • Assumptions/dependencies: execution sandboxes; secure repository access; reward proxies (closed issues, reduced review cycles); robust integration with tooling (linters, tests)
  • Chatbot governance and compliance auditing
    • Sectors: enterprise AI governance, trust & safety
    • What to build: a “Critic-as-a-Guardrail” service that generates textual justifications before executing actions; pre-deployment audits of agents with explainable critiques; action gating based on critic sentiment
    • Workflow: train critic on known policy rules and historical violations; integrate gating thresholds (sentiment scores) into agent runtime; human-in-the-loop review of flagged steps
    • Assumptions/dependencies: codified policies; reliability of sentiment mapping; escalation workflows for ambiguous cases
  • Interpretability and safety logging
    • Sectors: risk, compliance, AI operations
    • What to build: explainability reports of agent decisions (why a step is risky or suboptimal); “Critique Logs” attached to each action for postmortems and monitoring
    • Workflow: persist critic outputs alongside actions; aggregate critiques by failure mode; use prioritized replay for retraining on high-risk samples
    • Assumptions/dependencies: storage and observability; human review capacity; correctness of critic explanations
  • NLAC training library for off-policy agent fine-tuning
    • Sectors: software (ML platforms), academia
    • What to build: a reusable toolkit implementing the language successor model, language Bellman backup, evaluator aggregation, refinement distillation, and prioritized replay
    • Workflow: plug-and-play training over existing logs without costly on-policy sampling; support for multiple environments (dialog, tool-use, web)
    • Assumptions/dependencies: LLM training/inference resources; curated datasets; prompt engineering competence; mitigation of catastrophic forgetting

Long-Term Applications

These applications are promising but require further research, scaling, or regulatory validation. Each item includes sector links, prospective products/workflows, and critical dependencies.

  • Healthcare triage and care navigation agents
    • Sectors: healthcare
    • Vision: multi-step agents that coordinate EHR queries, scheduling, eligibility checks, and patient messaging while complying with clinical protocols; critic provides explainable safety checks at each step
    • Workflow: off-policy training from clinical operations logs; successor modeling of downstream clinical outcomes and compliance; refinement to avoid unsafe decisions
    • Dependencies: HIPAA-compliant data pipelines; clinical validation; FDA/regulatory scrutiny; robust reward design for patient outcomes; strong grounding to medical knowledge
  • Financial services support and decisioning
    • Sectors: finance (banking, insurance, fintech)
    • Vision: agents that handle KYC, claims, loan servicing, and policy-bound tool-use; textual critic justifications serve as audit trails; long-horizon decision support in risk workflows
    • Workflow: batch training from historical cases; gating actions with critic sentiment; human escalation for high-risk steps
    • Dependencies: strict compliance and auditability; accurate modeling of financial policies; data privacy; regulator acceptance; avoidance of speculative decision agents (e.g., trading)
  • Robotics and embodied decision-making
    • Sectors: robotics, industrial automation
    • Vision: textual planners that predict possible futures (via language successor models) to guide high-level policies for robots; critic rationales help reduce blind exploration in complex environments
    • Workflow: couple NLAC with grounded perception/action layers; use simulation logs for off-policy training; deploy refinement to improve task sequences
    • Dependencies: reliable grounding from language to control; sim-to-real transfer; robust transition modeling; safety certification
  • Multi-agent orchestration and governance
    • Sectors: software platforms, operations
    • Vision: critics mediating between multiple specialized agents (retrievers, solvers, callers), providing textual justifications to coordinate and arbitrate agent actions
    • Workflow: centralized “Critic Controller” that evaluates agent proposals and triggers refinements; off-policy learning from multi-agent traces
    • Dependencies: scalable coordination frameworks; latency and cost management; conflict resolution protocols
  • Automated scientific workflows and discovery
    • Sectors: R&D, biotech, materials
    • Vision: lab agents that plan experiments, query instruments, and analyze results with explainable action critiques; refine plans to improve sample efficiency and reproducibility
    • Workflow: off-policy training from lab notebooks and instrument logs; successor modeling of experimental outcomes; refinement to optimize multi-step protocols
    • Dependencies: high-fidelity simulators or rich historical logs; domain-grounded reward models; rigorous human oversight
  • Government and e-services policy-bound agents
    • Sectors: public sector
    • Vision: agents that navigate complex eligibility rules, document collection, and case management; critic provides transparent reasonings for compliance and fairness
    • Workflow: train on anonymized case logs; integrate action gating; provide clear justifications for every decision point
    • Dependencies: regulatory approval; fairness audits; privacy-by-design; standardized policy encodings
  • Enterprise-wide knowledge management and process optimization
    • Sectors: cross-industry enterprises
    • Vision: off-policy training across diverse departmental logs to build agents that optimize multi-step processes (procurement, onboarding, incident response) with explainable refinements
    • Workflow: unified replay buffers; task-specific reward shaping; critic-guided process redesign
    • Dependencies: data harmonization; secure data sharing; generalization across domains; continual learning and catastrophic forgetting mitigation
  • Standardized evaluation and benchmarks for language-space RL
    • Sectors: academia, standards bodies
    • Vision: shared tasks and datasets that test language successor modeling, language Bellman backups, and refinement efficacy across tool-use and dialog environments
    • Workflow: community benchmarks; reproducible pipelines; ablations (e.g., sentiment ordering, k-sample futures)
    • Dependencies: consensus on metrics; open datasets; cost-effective training resources
  • Tool ecosystem products
    • Sectors: software
    • Vision:
    • “Critic-as-a-Service” for explainable, step-level evaluations and guardrails
    • “Language Successor Simulator” to forecast multi-step outcomes for agents
    • “Refinement Engine” to iteratively improve proposed actions in production
    • Workflow: API-first services integrated into existing agent stacks
    • Dependencies: sustained inference budgets; robust privacy and security; reliability guarantees

Cross-cutting assumptions and dependencies

  • Base LLM capability: NLAC’s effectiveness depends on strong pretrained reasoning and the ability to process and generate coherent critiques and futures.
  • Off-policy data quality: Successor modeling and refinement hinge on representative logs with sufficiently informative reward signals; weak or biased logs can degrade performance.
  • Sentiment ordering: Many policy improvements assume textual critiques can be mapped to a consistent scalar ordering; failures in sentiment mapping affect selection/gating.
  • Successor accuracy: The language successor model must produce plausible futures; systematic errors can misguide refinement.
  • Tool integration: Real-world deployments require robust API access, error handling, and transactional integrity across tools.
  • Safety and compliance: High-stakes domains (healthcare, finance, public services) require rigorous validation, audits, and regulatory approvals.
  • Continual learning: Mitigation of catastrophic forgetting (e.g., rehearsal or LwF) is necessary for long-lived agents trained across tasks and time.
  • Cost and latency: Aggregating futures and critiques (k-sampling) adds inference overhead; practical systems must balance performance with compute budgets.
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