Assistance Regret in AI Decision-Making

• Assistance regret is defined as the performance gap between the cumulative rewards of an assistant’s actual actions and those of an optimal joint policy in hindsight.
• It is measured using various comparator benchmarks, including joint human–assistant policies, mentor trajectories, and oracle baselines, analyzed through methods like online submodular maximization and tracking regret.
• Its applications span decentralized learning, human–AI confidence alignment, safe reinforcement learning, and effective task delegation in sequential decision-making environments.

Searching arXiv for papers on assistance regret and closely related regret formulations. First, I’ll look for papers explicitly using the term “assistance regret.” arxiv_search(query="assistance regret", max_results=10, sort_by="submittedDate")

Assistance regret is a comparator-based notion of performance loss for settings in which one agent, model, or policy assists another under informational asymmetry, limited communication, or constrained delegation. In its most explicit recent formulation, it is “the gap between the cumulative utility of interactions and that of the optimal joint policies in hindsight, which map latent states to action pairs” (Ananthakrishnan et al., 9 Jul 2026). Closely related formulations measure the expected cumulative difference between executed and optimal decisions in AI-assisted contextual learning (Benz et al., 12 May 2026), the reward gap between an agent and a mentor in general Markov decision processes (Plaut et al., 19 Feb 2025), or the cumulative-reward shortfall of an assistant relative to oracle or automation baselines in sequential advisory settings (Peuter et al., 2022). This suggests that assistance regret is best understood not as a single canonical formula, but as a family of regret criteria specialized to assistance problems.

1. Comparator structure and core formulations

Across the literature, assistance regret is defined by the choice of comparator. The comparator may be the best joint human–assistant policy in hindsight, an optimal contextual policy, a mentor policy, or an oracle benchmark. The common structure is a gap between realized assisted performance and a stronger benchmark that is unavailable online.

Setting	Regret formulation	Comparator
Repeated assistance games (Ananthakrishnan et al., 9 Jul 2026)	$$R^\alpha_T(\chi)=\alpha \cdot \left( \max_{\pi_H^* \in \Pi_H, \pi_A^* \in \Pi_A} \sum_{t=1}^T r\left( \pi_H^*, \pi_A^*; \theta^{(t)} \right) \right) - \sum_{t=1}^T r\left( \pi_H^{(t)}, \pi_A^{(t)}; \theta^{(t)} \right)$$	Best fixed human and assistant policies in hindsight
AI assistance under human-alignment (Benz et al., 12 May 2026)	$\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$	Optimal policy $\pi^*$
Mentor-assisted RL (Plaut et al., 19 Feb 2025)	$R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$	Mentor trajectory
Zero-shot assistance (Peuter et al., 2022)	$$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$	Oracle or automation baseline

These formulations differ in whether the benchmark is joint, individual, causal, or oracle-based, but all treat regret as a shortfall relative to a benchmark that captures what stronger information, stronger coordination, or stronger planning could have achieved.

2. Assistance regret in repeated assistance games

The most formal and general recent use of the term appears in repeated assistance games, where an informed agent and an uninformed agent repeatedly interact over $T$ timesteps to optimize a common reward function; the informed agent observes a latent state of the world, while the uninformed agent observes only the human’s actions (Ananthakrishnan et al., 9 Jul 2026). With latent-state space $\Theta$, human policy class $\Pi_H$, and assistant policy class $\Pi_A$, the paper defines $\alpha$-assistance regret by

$\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$0

where $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$1.

The main algorithmic results are both decentralized and approximation-theoretic. The paper gives polynomial-time decentralized learning algorithms for both the human and assistant that achieve $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$2-approximate assistance regret at a rate of $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$3, more precisely

$\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$4

where $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$5 and $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$6 are the sizes of the human and assistant action spaces. In a pseudo-decentralized setting with a shared random string, the rate improves to

$\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$7

that is, a near-optimal $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$8 rate. The same work proves that achieving a regret approximation factor better than $\EE[R(T)]=\EE_{h_t,b_t \sim P(H,B)} \Bigg[ \sum_{t=1}^T \big( \mu(\pi^*(h_t,b_t)| h_t,b_t) - \EE_{a_t\sim P(A_t | h_t, b_t)} [ \mu(a_t| h_t,b_t) ] \big) \Bigg]$9 is computationally intractable unless $\pi^*$0.

Methodologically, these guarantees are obtained through a reduction to online submodular maximization under matroid constraints. The paper introduces the “Assistance Matroid,” shows that the space of feasible joint policies forms a partition matroid, and characterizes the reward-maximization objective as a weighted threshold potential. Its stable-adaptive decomposition writes assistance regret in terms of the centralized algorithm’s external regret, the assistant’s tracking regret, and the number of policy switches. This places assistance regret at the intersection of decentralized learning, online submodular maximization, and tracking-regret analysis.

3. Human–AI confidence alignment and zero-shot assistance

A second major line of work studies assistance regret in repeated human–AI decision-making with confidence signals. In the binary-prediction, binary-decision setting, the problem is equivalent to a two-armed online contextual learning problem with full feedback, where the context is the pair $\pi^*$1 of human and AI confidence (Benz et al., 12 May 2026). The general lower bound is

$\pi^*$2

Under perfect alignment between AI confidence and human confidence, the optimal policy has threshold structure,

$\pi^*$3

and an efficient algorithm attains regret

$\pi^*$4

When $\pi^*$5 and $\pi^*$6 is countable, a non-trivial generalization of the Dvoretzky–Kiefer–Wolfowitz inequality yields

$\pi^*$7

The same work bounds the performance gap under imperfect alignment in terms of Maximum Alignment Error:

$\pi^*$8

The central implication is that alignment can reduce the complexity of learning to make decisions with AI assistance.

A related sequential formulation appears in zero-shot assistance for new sequential decision problems, where the assistant advises rather than replaces the agent and must account for potential biases that may cause the agent to reject advice (Peuter et al., 2022). The assistant’s problem is modeled as a Generalized Hidden Parameter MDP,

$\pi^*$9

with unknown reward and bias parameters. Advice acceptance is modeled by

$R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$0

The paper reports that the proposed AIAD assistant adapts to agent biases and yields higher cumulative reward than automation-based alternatives. In inventory management, AIAD achieved $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$1, AIAD + automation $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$2, unassisted $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$3, IRL + automation $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$4, partial automation $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$5, and oracle + automation $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$6. It also shows that combining advice and automation outperforms advice alone at the cost of losing some safety guarantees.

Taken together, these works tie assistance regret to two distinct but compatible structures: learnability under aligned confidence signals, and adaptation to unknown reward and bias parameters in advisory sequential decision-making.

4. Asking for help, safety, and no-regret in general MDPs

In reinforcement learning, assistance regret has been formalized as the reward gap between an agent and a mentor when the agent is allowed to ask for help in a general MDP (Plaut et al., 19 Feb 2025). The setting allows irrecoverable or catastrophic errors, so the standard assumption that all errors are recoverable is explicitly discarded. The agent may query a mentor policy $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$7, and the objectives are both self-sufficiency and no-regret:

$R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$8

Self-sufficiency means the rate of mentor queries goes to zero, and no-regret means $R_T(M, \pi^m) = \E\left[ \sum_{t=1}^T r(s_t^m, \pi^m(s_t^m)) - \sum_{t=1}^T r(s_t, a_t) \right]$9.

The central theorem states that any algorithm that avoids catastrophe with $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$0 mentor queries is also a no-regret algorithm for MDPs, with

$$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$1

where $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$2 is additive catastrophe regret. The paper further states that this yields the first no-regret guarantee for general MDPs, including MDPs with irreversible costs. Its proof decomposes regret into state-based regret and action-based regret, and uses local generalization for the transition kernel,

$$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$3

This line of work is significant because it reframes assistance not as an obstacle to autonomy but as a mechanism for safe asymptotic self-sufficiency. In this formulation, the assistant is not merely a benchmark; the ability to query assistance is itself the structural condition that makes sublinear regret possible in unknown, unbounded, and high-stakes environments.

5. Deferral, allocation, and regret-averse targeting

Assistance regret also appears in problems where assistance takes the form of selective deferral or constrained policy targeting. In regression under human assistance, the goal is to jointly choose a subset of instances to outsource to humans and ridge-regression parameters for the remaining instances (De et al., 2019). With outsourced subset $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$4 and model parameters $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$5, the objective is

$$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$6

The problem is shown to be NP-hard, but the objective admits an alternative representation as a difference of nondecreasing submodular functions, is nondecreasing, and satisfies $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$7-submodularity. These properties yield a simple and efficient greedy algorithm with approximation guarantees. Empirically, the algorithm outsources to humans those samples in which the prediction error of the ridge regression model would have been the highest if it had to make a prediction, and it outperforms several competitive baselines in medical diagnosis and content moderation.

In policy targeting with regret aversion, the planner observes a rich feature set $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$8 in training data but can implement assignment rules only as a function of a subset $$\text{Assistance Regret} = \text{Cumulative Reward}_{\text{oracle}} - \text{Cumulative Reward}_{\text{assistant}}$$9 (Kitagawa et al., 19 Jun 2025). Regret for group $T$0 is defined by

$T$1

and the population regret-averse risk is

$T$2

For $T$3, the optimal rule treats all or none within each $T$4; for $T$5, unless all $T$6 within $T$7 have effects of the same sign, the optimal rule is fractional. For $T$8,

$T$9

The paper proposes a debiased empirical risk minimization approach with cross-fitting and establishes new upper and lower bounds for the excess risk, indicating a convergence rate of $\Theta$0 and asymptotic efficiency in certain cases.

These formulations extend assistance regret beyond explicit human–assistant games. Here, the shortfall arises because prediction or assignment must be mediated by a limited interface: a human budget, a coarse feature set, or a constrained deferral mechanism.

6. System-level failure detection and related regret machinery

A further use of regret in assistance systems is diagnostic rather than purely evaluative. In human–robot interaction, system-level regret is proposed as a metric for detecting prediction failures that actually degrade closed-loop robot performance (Nakamura et al., 2024). At time $\Theta$1, regret is defined by

$\Theta$2

which can be used with reward-based planners through the Luce-Shepard choice rule,

$\Theta$3

The paper identifies high-regret interactions as precisely those in which mispredictions degraded closed-loop robot performance, and reports that fine-tuning with the informative but significantly smaller high-regret data, 23% of deployment data, is competitive with fine-tuning on the full deployment dataset.

Beyond assistance-specific papers, several regret frameworks supply the mathematical background against which assistance regret is formulated. Dynamic regret in infinite-horizon LQR is defined as the difference between the LQR cost of a causal controller and the LQR cost of the unique clairvoyant non-causal controller, and the regret-optimal controller is obtained via a reduction to a Nehari extension problem (Sabag et al., 2021). Discounted-sum games define regret as

$\Theta$4

and identify “optipess” strategies that first assume the environment is collaborating, then assume it is adversarial (Cadilhac et al., 2018). Regret-based reward elicitation for MDPs defines minimax regret by

$\Theta$5

and uses regret-reduction to choose bound queries (Regan et al., 2012). In model-free RL and games, ARMAC replaces explicit cumulative-regret storage by conditional advantage estimation and regret matching, using a buffer of past policies rather than importance sampling (Gruslys et al., 2020). In risk-aware LQ control, distributional regret quantifies the price paid for not knowing the exact probability distribution and is defined through worst case Conditional Value-at-Risk; its regret bound increases with tighter risk level (Renganathan et al., 2022).

These neighboring literatures do not use a single assistance-regret formalism, but they establish the recurring ingredients that assistance-regret work reuses: clairvoyant or hindsight comparators, minimax or approximate benchmarks, structured no-regret learning, and regret-guided information acquisition. A plausible implication is that assistance regret functions as a unifying bridge between cooperative decision-making, safe delegation, and comparator-based control under partial information.