reinforcement learning engineers

Abstract: The last decade has seen the development of powerful methods for learning complex structure from high-dimensional data. These advances have brought to the foreground fundamental connections between subdisciplines of physics, applied mathematics, and machine learning. In this review, we bring together some of these ideas, often expressed in different languages, to highlight a conceptual thread that links five distinct fields: control theory, optimal transport, probabilistic inference, non-equilibrium thermodynamics, and machine learning. A common theme is the optimization of free-energy-like functionals under dynamical or statistical constraints. We offer a guided tour through this thread and present selected applications in reinforcement learning, variational inference, and generative modeling. The review does not assume prior familiarity with these topics, and begins with principles originating from physics.

Abstract: For constant-stepsize stochastic approximation (SA), the iterates converge in distribution to a stationary law that depends on the stepsize $α.$ Steady-state convergence (SSC) concerns the limit of the scaled stationary distribution as $α\downarrow 0.$ Existing SSC theory requires i.i.d. or additive noise and global differentiability of the mean operator, and yields suboptimal rates. We develop a unified SSC theory for constant-stepsize contractive SA driven by Markovian, multiplicative noise, covering both locally differentiable and locally nondifferentiable mean operators. A key methodological contribution is a multi-step universality framework that progressively reduces the original stochastic recursion to tractable auxiliary dynamics while preserving its steady-state limit. Under local quadratic linearization at the fixed point, we obtain a Gaussian approximation of the scaled steady state at the optimal rate $O(\sqrtα)$ in Wasserstein-2 distance, which further gives finite-time Gaussian approximations for the raw iterates. In the locally nondifferentiable regime, we establish a general SSC result and show that the leading-order asymptotic bias can be of order $\sqrtα$, in contrast to the $α$-order bias in the smooth regime. We apply the theory to Markovian linear SA and asynchronous Q-learning, neither of which is covered by prior results. We further propose a bias-reduction scheme for Q-learning that requires no knowledge of the local smoothness regime, validated by numerical experiments.

Abstract: Combining search with function approximation has driven major advances in game-playing programs, making self-play algorithms more competitive than ever. Still, the computational overhead of the most popular methods, based on Monte Carlo Tree Search (MCTS), can be substantial. In this work, we investigate whether simpler methods remain competitive in non-trivial, moderately sized games such as Connect Four, Hex(7x7) and synthetic games. We train a minimal self-play implementation of Approximate Value Iteration (AVI) and use ground-truth oracles for exact evaluation. Contrary to expectations, our results demonstrate the surprising effectiveness of AVI: it learns more accurate value functions than those learned by AlphaZero, while its one-step-lookahead greedy policies remain competitive with MCTS-based policies at substantially lower training and inference costs. Preliminary experiments on Othello and Go(9x9) show that AVI trains stably on larger games and learns effective value functions. These findings suggest that the success of MCTS-based methods may have eclipsed simpler approaches that have become increasingly practical with modern deep-learning tools.

Abstract: While many video-game environments (VGEs) have played crucial roles in advancing reinforcement learning (RL), developing novel VGEs or modifying existing ones to support new features, has been a laborious process requiring extensive hand-coding. Here we present PlayTrain, an RL framework that combines the abilities of large language models (LLMs) to robustly generate JavaScript (JS) games from a minimal human prompt, and an efficient pipeline that can run any JS game in a standard 'gym' environment. Not only are recent LLMs particularly good at writing JS code, but the JS format also allows users to easily play generated VGEs, while PlayTrain enables us to train RL agents on the exact same games. We demonstrate multiple use cases of PlayTrain, including cloning well-known Atari and ProcGen games in simple JS, where PlayTrain trains pixel-based agents end-to-end at over 1M agent-decisions per second on a single GPU node; and creating modified versions thereof (e.g., that support novel test sets, procedural generation logics, or game dynamics). Through PlayTrain, we reimagine RL VGE development: all we need is a single JS file, generated and modified through an LLM. We discuss promising future RL research directions that PlayTrain unlocks.

Abstract: Solving Nash equilibria for general multi-player Markov games is computationally intractable, while two-player zero-sum Markov games admit fast last-iterate policy-optimization methods. Finite-horizon zero-sum networked separable Markov games occupy an important middle ground: they retain global competition structure through pairwise interactions, while preserving computational tractability of Nash equilibria (NE) in the full-information and known-transition setting. Existing algorithms for this class either proceed through equilibrium-collapse arguments for a simplified setting where a single controller determines the transition probability, or backward dynamic programming that relies on equilibrium solvers at each stage. However, the design and analysis of direct policy-update approaches remain inadequate. To address this issue, we propose the entropy-regularized optimistic multiplicative weights update (ER-OMWU), a complementary single-loop policy dynamic that updates players' policies symmetrically and returns an approximate NE in the last iteration. We provide a first last-iterate convergence analysis of policy dynamics in the games of interest: after $\widetilde{O}(1/ε)$ iterations, the returned policy is an $ε$-approximate Nash equilibrium. The result preserves the near-linear convergence rate achieved by policy optimization in two-player zero-sum Markov games, but extends the policy-dynamics viewpoint to a more complicated but structured multi-player setting.