Sequential Decision-Making Models

• Sequential decision-making models are mathematical frameworks that formalize decision processes over time by defining states, actions, rewards, and transition dynamics.
• They underpin advanced methodologies such as model-based and model-free reinforcement learning, offering robust policy optimization and regret minimization.
• These models are applied in diverse fields like robotics, precision agriculture, and human-AI collaboration, providing theoretical guarantees and scalable algorithms.

Sequential decision-making models formally describe processes in which an agent or system takes a sequence of actions over time to achieve specific objectives, accounting for feedback, uncertainty, and interactions with a dynamic environment. A central challenge in these models is to determine effective strategies (policies) that make optimal or near-optimal choices at each step, given current information and knowledge of the system’s dynamics, possible rewards, and in some cases the reactions of other agents or changes in underlying conditions. This class of models underpins key areas of research and application in artificial intelligence, control theory, operations research, and the behavioral sciences.

1. Foundations and Core Formulations

Sequential decision-making models are generally formalized using controlled stochastic processes, most notably Markov Decision Processes (MDPs) and their extensions. An MDP is defined by a tuple $(\mathcal{S}, \mathcal{A}, T, R, \gamma)$, where $\mathcal{S}$ is the state space, $\mathcal{A}$ the action space, $T$ the (possibly stochastic) transition function, $R$ the reward function, and $\gamma \in [0, 1)$ a discount factor. At each time $t$, the agent observes a state $s_t$, selects an action $a_t$, receives an immediate reward $R(s_t, a_t)$, and transitions to $s_{t+1} \sim T(\cdot|s_t, a_t)$.

Key elements include:

• Policies: A (possibly stochastic) mapping $\pi: \mathcal{S} \to \mathrm{Pr}(\mathcal{A})$ defining the agent’s behavior.
• Value Functions: The expected cumulative (discounted) reward, $$V^{\pi}(s) = \mathbb{E}^{\pi}\left[\sum_{t=0}^\infty \gamma^t R(s_t, a_t) | s_0 = s\right]$$.
• Optimality Criteria: Typically maximizing expected cumulative reward (but can be extended to multi-objective, risk-sensitive, or constrained formulations (Roijers et al., 2014, Rosemberg et al., 23 May 2024)).

Extensions include partially observable MDPs (POMDPs), multi-agent systems (Markov games), and models with explicit consideration of model uncertainty or information acquisition (Liu et al., 2022, Xu et al., 2023).

2. Learning and Optimization Methodologies

Sequential decision-making problems are commonly addressed via planning and reinforcement learning (RL), with major lines including:

• Model-Based RL: Learns or exploits a known transition model, either for planning (tree search, dynamic programming) or for computing policy/value functions via simulation (Liu et al., 2022). The OMLE algorithm, for example, unifies optimism-driven exploration with maximum likelihood model estimation and addresses both fully and partially observable settings under the SAIL condition, with guarantees independent of observation space size (Liu et al., 2022).
• Model-Free RL: Directly optimizes policies or action-values from interaction (without explicit model learning), often using temporal-difference learning or policy gradient methods.
• Regret Minimization: Particularly in extensive-form games (tree-form), algorithms such as counterfactual regret minimization (CFR) provide strong guarantees for equilibrium computation. Recent advances remove the requirement for a fixed decision tree, enabling sublinear regret bounds in unknown or dynamically constructed spaces (Farina et al., 2021).
• Bandit and Exploration-Exploitation Algorithms: In contexts with limited data, model-based bandits with domain-informed nonlinear response curves (e.g., Mitscherlich or Michaelis-Menten in agriculture) can embed mechanistic prior knowledge for improved sample efficiency (Arya et al., 2 Sep 2025). Contextual bandit frameworks can be augmented with LLMs for efficient, high-reward early decisions, then adaptively shift to learned strategies (Chen et al., 17 Jun 2024).
• Multi-Objective and Constrained Optimization: Scalarization techniques convert vector-valued reward functions into single objectives (when linear), or require Pareto front or coverage set computation (for monotonic/nonlinear scalarizations). Problem taxonomy includes known tradeoff weights, decision support, and policies that may be deterministic, stochastic, or nonstationary (Roijers et al., 2014, Rosemberg et al., 23 May 2024).

3. Human-AI Interaction, Teaching, and Explanation

In addition to pure optimization, sequential decision-making models increasingly handle teaching (demonstration), explanation, and human-in-the-loop design:

• Dynamic Teaching Dimension Models: The teacher is actively modeled as a decision maker who crafts informative sequences of demonstrations, extending concepts like teaching dimension (TD) and subset teaching dimension (STD) into noisy and sequential Markovian environments. Teaching efficiency can be significantly improved by focusing on sequences (teaching trails) rather than fixed policy demonstration—Algorithm 1 in (Walsh et al., 2012) provides a practical heuristic.
• Counterfactual and Causal Explanations: New frameworks integrate structural causal models (SCM) with MDPs to provide actual, weak, and responsibility-based causes for agent actions, capturing explanations across state factors, rewards, transitions, and future value. Algorithmic contributions include approximate and exact methods for determining explanatory sets, supported by experimental user studies (Nashed et al., 2022), and dynamic programming for counterfactual explanations under k-change constraints (Tsirtsis et al., 2021).
• Learning-to-Defer and Human Oversight: Sequential learning-to-defer (SLTD) models decide adaptively when to defer control to human experts, accounting for nonstationary dynamics and long-term outcomes. This is formalized as a model-based RL problem with deferral triggers based on predictive distributions over value differences, propagating epistemic and aleatoric uncertainties for interpretability (Joshi et al., 2021).

4. Algorithmic Advances and Efficient Training

Recent trends emphasize scalability, sample efficiency, and the integration of advanced function approximation or policy representation:

• Large Sequence Models and Transformers: Transformer-based architectures have emerged as powerful “decision transformers,” enabling sequence modeling of state-action-reward tuples, improved credit assignment via attention, and enhanced handling of partial observability by attending to entire observation histories. Training and systems challenges include efficient parallelism, massive dataset streaming, and maintaining sample efficiency (Wen et al., 2023).
• Constraint Handling with Duality: For constrained MDPs with nonlinear constraints (CMDPs), Two-Stage Deep Decision Rules (TS-DDR) offer a principled approach by training parameterized neural policies via Lagrangian duality. Forward passes solve deterministic optimization problems for feasibility, while backward passes use dual gradients to update policy parameters, greatly increasing computational speed and solution quality in high-stakes applications (e.g., long-term hydrothermal dispatch) (Rosemberg et al., 23 May 2024).
• Post-Training and Fine-Tuning of LLMs: RL-based post-training methods (such as DPO, GRPO, TBA) enable smaller LLMs to achieve performance competitive with much larger models in sequential tasks, by addressing credit assignment and leveraging token-level or episode-level rewards. Hierarchical RL further decomposes agent tasks into high-level planning and low-level sequence generation steps (Dilkes et al., 14 Aug 2025).
• Reduction-based Approaches: Frameworks that convert algorithms for instantaneous feedback to handle delayed feedback achieve regret bounds matching or improving upon prior work. By timing updates according to when feedback becomes available, these approaches are robust to delays in both finite and function-approximation settings (Yang et al., 2023).

5. Applications and Domain-Specific Extensions

Sequential decision-making models are fundamental across a range of domains:

• Robotics and Control: Meta-level control schedules deliberation and resource allocation for time-critical sequential decision making, e.g., mobile-robot path planning, using envelope alteration and policy generation routines. Precursor and recurrent models cater to offline and online interleaving of planning and execution, with algorithmic support for performance-cost trade-offs (Dean et al., 2013).
• Precision Agriculture and Environmental Management: Nonlinear bandit algorithms embedded with agronomic response curves optimize fertilizer input decisions, supporting sustainable and resource-constrained agricultural practices (Arya et al., 2 Sep 2025).
• Human–Machine Interaction: Counterfactual decision models, perimeter identification via traffic data (Taitler, 4 Sep 2024), and sequential decision-making for inline text autocomplete with cognitive load-penalized rewards (Chitnis et al., 21 Mar 2024) exemplify adaptation of the frameworks for user-centric objectives and domain constraints.
• Multi-Agent Systems and Game Theory: Model-free regret minimization without prior model knowledge yields sublinear regret in tree-form sequential decision settings (including Nash equilibrium computation), with robust performance in adversarial, partially observable, and dynamic environments (Farina et al., 2021).
• Sequential Information Acquisition: Nested optimal stopping approaches with two-stage (coarse and refined) information regimes capture real-world processes such as e-commerce product selection, financial investment, and healthcare treatment planning, analyzed with viscosity solution techniques (Xu et al., 2023).

6. Theoretical Guarantees and Structural Insights

Sequential decision-making models are often supported by rigorous mathematical bounds and insights:

• Sample Complexity and Regret: Tight minimax regret and sample complexity bounds exist across various settings, from model-based RL under the SAIL condition and well-conditioned predictive state representations (PSRs) (Liu et al., 2022) to sublinear regret guarantees in unknown tree-structured domains (Farina et al., 2021).
• Teaching Dimension and Learnability: Extensions of teaching dimension notions to noisy and sequential environments yield improved sample complexity bounds for teaching RL model classes, with explicit formulae such as $$m = H(\epsilon, \delta) = O((1/\epsilon^2)\log(1/\delta))$$ in coin learning and $k \cdot H(\epsilon, \delta/k)$ in k-armed bandits (Walsh et al., 2012).
• Utility Theory Extensions: Sequential utility theory generalizes the VNM theorem, revealing that additive reward structures require stronger preference axioms than the Markov memorylessness property alone. Affine-Reward MDPs allow for multiplicative factors in utility accumulation, and goal-seeking constraints recover potential-based forms (Shakerinava et al., 2022).
• Multi-Objective and Constrained Analysis: Scalarization choices determine the structure of optimal policy sets, with fundamental differences in policy requirements and solution concepts (coverage set, Pareto front) contingent on the linearity or monotonicity of scalarization functions (Roijers et al., 2014, Rosemberg et al., 23 May 2024).

7. Implications, Open Challenges, and Future Directions

As sequential decision-making models mature, research continues on several fronts:

• Unified Large Decision Models: Analogous to large language and vision models, the development of “large decision models” that generalize across diverse tasks, environments, and objectives—while maintaining sample efficiency and interpretability—remains a key goal (Wen et al., 2023).
• Scalability with Limited Data: Leveraging domain knowledge through model-based and mechanistic approaches enables practical deployment in low-data, resource-constrained settings, particularly in sustainability domains (Arya et al., 2 Sep 2025).
• Explanability and Trust: Rich structural causal models and counterfactual analysis are being integrated into agent policies, supporting transparency and facilitating human understanding and oversight (Tsirtsis et al., 2021, Nashed et al., 2022).
• Efficient Computation and Real-Time Applications: New training paradigms (duality-driven, online selection, reduction-based for delays) enable tractable deployment of previously intractable models in real-time and high-dimensional contexts, with continuing progress expected in hardware–software codesign (Rosemberg et al., 23 May 2024, Chen et al., 17 Jun 2024, Yang et al., 2023).
• Human-AI Collaboration and Deferral: Sequential learning-to-defer, preemptive intervention, and policy adaptation to nonstationary environments are raising the bar for safe and reliable four-stage human–AI systems in high-stakes applications (Joshi et al., 2021).

Overall, sequential decision-making models—grounded in rigorous mathematical theory, realized via advanced algorithms, and extended through domain knowledge and human collaboration—form the core of agentic AI systems, enabling adaptive and optimal decision processes under uncertainty, partial information, and real-time constraints.