Max Horwitz

Jake Gonzales, Max Horwitz, Eric Mazumdar et al.

Provably efficient and robust equilibrium computation in general-sum Markov games remains a core challenge in multi-agent reinforcement learning. Nash equilibrium is computationally intractable in general and brittle due to equilibrium multiplicity and sensitivity to approximation error. We study Risk-Sensitive Quantal Response Equilibrium (RQRE), which yields a unique, smooth solution under bounded rationality and risk sensitivity. We propose \texttt{RQRE-OVI}, an optimistic value iteration algorithm for computing RQRE with linear function approximation in large or continuous state spaces. Through finite-sample regret analysis, we establish convergence and explicitly characterize how sample complexity scales with rationality and risk-sensitivity parameters. The regret bounds reveal a quantitative tradeoff: increasing rationality tightens regret, while risk sensitivity induces regularization that enhances stability and robustness. This exposes a Pareto frontier between expected performance and robustness, with Nash recovered in the limit of perfect rationality and risk neutrality. We further show that the RQRE policy map is Lipschitz continuous in estimated payoffs, unlike Nash, and RQRE admits a distributionally robust optimization interpretation. Empirically, we demonstrate that \texttt{RQRE-OVI} achieves competitive performance under self-play while producing substantially more robust behavior under cross-play compared to Nash-based approaches. These results suggest \texttt{RQRE-OVI} offers a principled, scalable, and tunable path for equilibrium learning with improved robustness and generalization.

Max Horwitz, Jake Gonzales, Eric Mazumdar et al.

A growing line of work reframes preference-based fine-tuning of large language models game-theoretically: Nash Learning from Human Feedback (NLHF) recasts the problem as a zero-sum game over policies. However, optimization is over expected pairwise payoffs, thereby conflating policies with similar win rates but different tail behavior. As such, these methods are agnostic to where in the data distribution they succeed or fail: strong average performance can mask systematic failure across prompts, annotators, or safety-critical strata. We introduce risk-sensitive preference games, in which players optimize convex risk measures of their preference loss, exploiting structure in preference uncertainty. While risk-sensitivity generally breaks the zero-sum structure, we show that translation invariance of many risk metrics ensures that we retain monotonicity, yielding fast convergence of sample-efficient self-play methods. Furthermore, we establish algorithmic stability and offline sample complexity bounds that scale with risk, requiring simultaneous control of structural bias from nonlinear risk transformations, statistical bias in risk estimation, and concentration tailored to the risk-sensitive setting. To address statistical bias, we introduce a hierarchical game formulation and a two-timescale extragradient algorithm with bias correction that converges to the Stackelberg equilibrium and is especially effective in low-sample regimes. Empirically, risk-adjusted policies are robust across data strata, stable across risk choices, and match or exceed risk-neutral performance thereby achieving robustness without a performance tax.