A Lecture Note on Offline RL and IRL, Part II: Foundations of Inverse Reinforcement Learning and Dynamic Discrete Choice Models

In the forward reinforcement-learning problem, the reward is fixed and known; the learner is asked to find a good policy or value function. Here we turn the question around. Given offline data generated by an expert, can we recover the reward the expert was optimizing? This is the inverse reinforcement learning problem, and remarkably, two communities, structural econometricians studying dynamic discrete choice (DDC) and machine learners studying entropy-regularized IRL, have been working on exactly the same probabilistic model under different names. We begin by proving their equivalence. We then develop the classical identification result of Magnac and Thesmar and the classical computational paradigms that grew out of it: Rust's nested fixed-point algorithm, the conditional-choice-probability approach of Hotz and Miller, and the two temporal-difference approaches of Adusumilli and Eckardt: linear semi-gradient TD and approximate value iteration. Each route has its limits: dimensionality, transition-kernel estimation, the deadly triad, or projected fixed-point bias. We then walk through the modern ML/IRL strand: adversarial IRL, occupancy matching, IQ-Learn, and offline ML-IRL, deriving each method's actual objective and stating precisely what it does and does not identify. We close with the empirical-risk-minimization framework of Kang et al., which yields a gradient-based estimator for offline IRL/DDC.

Reasonably reasoning AI agents can avoid game-theoretic failures in zero-shot, provably

AI agents are increasingly deployed in interactive economic environments characterized by repeated AI-AI interactions. Despite AI agents' advanced capabilities, empirical studies reveal that such interactions often fail to stably induce a strategic equilibrium, such as a Nash equilibrium. Post-training methods have been proposed to induce a strategic equilibrium; however, it remains impractical to uniformly apply an alignment method across diverse, independently developed AI models in strategic settings. In this paper, we provide theoretical and empirical evidence that off-the-shelf reasoning AI agents can achieve Nash-like play zero-shot, without explicit post-training. Specifically, we prove that `reasonably reasoning' agents, i.e., agents capable of forming beliefs about others' strategies from previous observation and learning to best respond to these beliefs, eventually behave along almost every realized play path in a way that is weakly close to a Nash equilibrium of the continuation game. In addition, we relax the common-knowledge payoff assumption by allowing stage payoffs to be unknown and by having each agent observe only its own privately realized stochastic payoffs, and we show that we can still achieve the same on-path Nash convergence guarantee. We then empirically validate the proposed theories by simulating five game scenarios, ranging from a repeated prisoner's dilemma game to stylized repeated marketing promotion games. Our findings suggest that AI agents naturally exhibit such reasoning patterns and therefore attain stable equilibrium behaviors intrinsically, obviating the need for universal alignment procedures in many real-world strategic interactions.

LLM Personas as a Substitute for Field Experiments in Method Benchmarking

Field experiments (A/B tests) are often the most credible benchmark for methods in societal systems, but their cost and latency create a major bottleneck for iterative method development. LLM-based persona simulation offers a cheap synthetic alternative, yet it is unclear whether replacing humans with personas preserves the benchmark interface that adaptive methods optimize against. We prove an if-and-only-if characterization: when (i) methods observe only the aggregate outcome (aggregate-only observation) and (ii) evaluation depends only on the submitted artifact and not on the algorithm's identity or provenance (algorithm-blind evaluation), swapping humans for personas is just panel change from the method's point of view, indistinguishable from changing the evaluation population (e.g., New York to Jakarta). Furthermore, we move from validity to usefulness: we define an information-theoretic discriminability of the induced aggregate channel and show that making persona benchmarking as decision-relevant as a field experiment is fundamentally a sample-size question, yielding explicit bounds on the number of independent persona evaluations required to reliably distinguish meaningfully different methods at a chosen resolution.

Bayesian Optimization in Language Space: An Eval-Efficient AI Self-Improvement Framework

Large Language Models (LLMs) have recently enabled self-improving AI, i.e., AI that iteratively generates, evaluates, and refines its own outcomes. Recent studies have shown that self-improving AI focusing on prompt optimization can outperform state-of-the-art reinforcement-learning fine-tuned LLMs. Here, their `performance' is typically measured by query efficiency - the number of LLM-generated solution samples required to meet a certain performance threshold. However, in many societal applications, the primary limitation is not generating new solutions but evaluating them. For instance, evaluating an ad's effectiveness requires significant human feedback, which is far more costly and time-consuming than generating a candidate ad. To optimize for the evaluation efficiency objective, a natural approach is to extend Bayesian Optimization (BO), a framework proven optimal for evaluation efficiency, to the language domain. However, the difficulty of directly estimating suitable acquisition functions in LLMs' minds makes this extension challenging. This paper overcomes this challenge by proving that the combination of the simple and widely used Best-of-N selection strategy and simple textual gradients (i.e., textual edits from a critic model) statistically emulates the behavior of the gradients on the canonical UCB acquisition function, which induces optimal exploration in terms of evaluation efficiency. Based on this result, we propose TextGrad-Best-of-N Bayesian Optimization (T-BoN BO), a simple and eval-efficient language-space Bayesian optimization framework for AI self-improvement. We also empirically validate T-BoN BO by applying it to automated ad alignment tasks for persona distribution, demonstrating its superior performance compared to popular state-of-the-art baselines.