arXiv subjects

Amy Greenwald

Publications and source records attributed to Amy Greenwald.

At least 19 recordsLinked to original sources

arXiv2026

Towards Learning Representations of Policies in Two-Player Zero-Sum Imperfect-Information Games

We investigate the problem of learning useful policy representations (embeddings) in two-player zero-sum imperfect-information games. We make three contributions: First, we introduce methods of creating datasets of policies for a given game. Second, we propose methods to learn policy representations. Third, we introduce downstream tasks to evaluate the effectiveness of such representations. We evaluate each dataset method, embedding method, and downstream task on Kuhn and Leduc Poker. Although our methods are very basic, we demonstrate that useful behavioral representations are present in the learned embeddings. To our knowledge, this work is among the first to systematically compare self-supervised learning techniques for learning policy representations in games. Our code is available at https://github.com/VitamintK/ssl-project for others to extend.

cs.LG↗

arXiv2026

Zero Collapse: A Failure Mode of Policy Gradient Methods in Discontinuous Reward Environments

Bidding in repeated auctions is a central challenge for reinforcement learning (RL), combining continuous control with the strategic complexities of digital advertising. While policy gradient and value-based methods seem well-suited for these settings, they often struggle with the discontinuous, "cliff-like" nature of auction reward landscapes. In a first-price auction, for example, a bidder receives zero reward until they cross a specific threshold, after which the reward decreases as the bid increases. This creates a landscape of flat, zero-reward regions separated by sharp boundaries. We identify a fundamental failure mode in this setting termed "zero collapse." We show that stochastic exploration and gradient-based updates can cause policies to overshoot optimal high-reward regions and enter flat, zero-reward regimes. Once there, the lack of an informative gradient signal makes recovery extremely sample-inefficient, effectively trapping the agent. We find that actor-critic methods are particularly susceptible, as biased value estimates can accelerate this movement toward unstable regions. Our contributions include: (1) a mechanistic explanation of how discontinuous rewards lead to vanishing signals and zero collapse; (2) an analysis of the interaction between policy stochasticity and step size; and (3) an empirical demonstration of this phenomenon across REINFORCE and actor-critic variants. We propose practical mitigation strategies involving initialization and architectural choices to improve stability. Finally, we introduce a formal RL framework for auction environments highlighting their unique structural properties.

cs.LG↗

arXiv2026

Distilling Game Code World Model Generation into Lightweight Large Language Models

Large Language Models (LLMs) have shown great ability in generating executable code from natural language, opening the possibility of automatically constructing environments for AI agents. Recent work on Code World Models (CWMs) demonstrates that LLMs can translate game rules into Python implementations compatible with solvers like Monte Carlo Tree Search. We study this problem in game settings, where generated environments must implement rules, legal actions, state transitions, observations, and rewards. We refer to these game-specific executable models as Game Code World Models (GameCWMs). However, current approaches to generating code world models rely on frontier models and inference-time refinement loops, limiting accessibility and scalability. This work investigates whether GameCWM generation capabilities can be distilled into smaller models through post-training. We introduce: (1) a curated dataset of 30 games spanning perfect and imperfect information games, (2) a verification framework that evaluates generated code against structural and semantic game properties, and (3) a post-training pipeline combining Supervised Fine-Tuning (SFT) with Reinforcement Learning with Verifiable Rewards (RLVR). We experiment with Qwen2.5-3B-Instruct and find that SFT can increase syntactic correctness, while RLVR can improve execution-level adherence to game rules, thereby improving Qwen's ability to generate valid GameCWMs in both perfect and imperfect information games. Overall, our pipeline makes Qwen2.5-3B-Instruct more capable of generating valid GameCWMs, thereby offering a scalable path toward automatic environment generation from natural language.

cs.AI↗

arXiv2026

Chronax: A Jax Library for Univariate Statistical Forecasting and Conformal Inference

Time-series forecasting is central to many scientific and industrial domains, such as energy systems, climate modeling, finance, and retail. While forecasting methods have evolved from classical statistical models to automated, and neural approaches, the surrounding software ecosystem remains anchored to the traditional Python numerical stack. Existing libraries rely on interpreter-driven execution and object-oriented abstractions, limiting composability, large-scale parallelism, and integration with modern differentiable and accelerator-oriented workflows. Meanwhile, today's forecasting increasingly involves large collections of heterogeneous time series data, irregular covariates, and frequent retraining, placing new demands on scalability and execution efficiency. JAX offers an alternative paradigm to traditional stateful numerical computation frameworks based on pure functions and program transformations such as just-in-time compilation and automatic vectorization, enabling end-to-end optimization across CPUs, GPUs, and TPUs. However, this modern paradigm has not yet been fully incorporated into the design of forecasting systems. We introduce Chronax, a JAX-native time-series forecasting library that rethinks forecasting abstractions around functional purity, composable transformations, and accelerator-ready execution. By representing preprocessing, modeling, and multi-horizon prediction as pure JAX functions, Chronax enables scalable multi-series forecasting, model-agnostic conformal uncertainty quantification, and seamless integration with modern machine learning and scientific computing pipelines.

cs.LG↗

arXiv2026

TempusBench: An Evaluation Framework for Time-Series Forecasting

Foundation models have transformed natural language processing and computer vision, and a rapidly growing literature on time-series foundation models (TSFMs) seeks to replicate this success in forecasting. While recent open-source models demonstrate the promise of TSFMs, the field lacks a comprehensive and community-accepted model evaluation framework. We see at least four major issues impeding progress on the development of such a framework. First, existing evaluation frameworks comprise benchmark forecasting tasks derived from often outdated datasets (e.g., M3), many of which lack clear metadata and overlap with the corpora used to pre-train TSFMs. Second, these frameworks evaluate models along a narrowly defined set of benchmark forecasting tasks, such as forecast horizon length or domain, but overlook core statistical properties such as non-stationarity and seasonality. Third, domain-specific models (e.g., XGBoost) are often compared unfairly, as existing frameworks do not enforce a systematic and consistent hyperparameter tuning convention for all models. Fourth, visualization tools for interpreting comparative performance are lacking. To address these issues, we introduce TempusBench, an open-source evaluation framework for TSFMs. TempusBench consists of 1) new datasets which are not included in existing TSFM pretraining corpora, 2) a set of novel benchmark tasks that go beyond existing ones, 3) a model evaluation pipeline with a standardized hyperparameter tuning protocol, and 4) a tensorboard-based visualization interface. We provide access to our code on GitHub: https://github.com/Smlcrm/TempusBench and maintain a live leaderboard at https://benchmark.smlcrm.com/.

cs.LG↗

arXiv2025

Spectral Collapse Drives Loss of Plasticity in Deep Continual Learning

We investigate why deep neural networks suffer from loss of plasticity in continual learning, and thus fail to learn new tasks without reinitializing parameters. We show that this failure is preceded by Hessian spectral collapse at new-task initialization, where meaningful curvature directions vanish and gradient descent becomes ineffective. Analyzing a linearized ReLU network, we derive explicit $\epsilon$-rank conditions for successful training and prove that the loss-weighted Gram matrix is spectrally equivalent to the Generalized Gauss-Newton approximation, thereby relating NTK dynamics to Hessian curvature. Targeting spectral collapse directly, we then discuss the Kronecker factored approximation of the Hessian, which motivates two regularization enhancements: maintaining high effective feature rank and applying L2 penalties. Experiments on continual supervised and reinforcement learning tasks confirm that combining these two regularizers effectively preserves plasticity.

cs.LG↗

arXiv2025

Bi-Level Policy Optimization with Nystr\"om Hypergradients

The dependency of the actor on the critic in actor-critic (AC) reinforcement learning means that AC can be characterized as a bilevel optimization (BLO) problem, also called a Stackelberg game. This characterization motivates two modifications to vanilla AC algorithms. First, the critic's update should be nested to learn a best response to the actor's policy. Second, the actor should update according to a hypergradient that takes changes in the critic's behavior into account. Computing this hypergradient involves finding an inverse Hessian vector product, a process that can be numerically unstable. We thus propose a new algorithm, Bilevel Policy Optimization with Nystr\"om Hypergradients (BLPO), which uses nesting to account for the nested structure of BLO, and leverages the Nystr\"om method to compute the hypergradient. Theoretically, we prove BLPO converges to (a point that satisfies the necessary conditions for) a local strong Stackelberg equilibrium in polynomial time with high probability, assuming a linear parametrization of the critic's objective. Empirically, we demonstrate that BLPO performs on par with or better than PPO on a variety of discrete and continuous control tasks.

cs.LG↗

arXiv2025

Infinite Horizon Markov Economies

In this paper, we study a generalization of Markov games and pseudo-games that we call Markov pseudo-games, which, like the former, captures time and uncertainty, and like the latter, allows for the players' actions to determine the set of actions available to the other players. In the same vein as Arrow and Debreu, we intend for this model to be rich enough to encapsulate a broad mathematical framework for modeling economies. We then prove the existence of a game-theoretic equilibrium in our model, which in turn implies the existence of a general equilibrium in the corresponding economies. Finally, going beyond Arrow and Debreu, we introduce a solution method for Markov pseudo-games and prove its polynomial-time convergence. We then provide an application of Markov pseudo-games to infinite-horizon Markov exchange economies, a stochastic economic model that extends Radner's stochastic exchange economy and Magill and Quinzii's infinite-horizon incomplete markets model. We show that under suitable assumptions, the solutions of any infinite-horizon Markov exchange economy (i.e., recursive Radner equilibria -- RRE) can be formulated as the solution to a concave Markov pseudo-game, thus establishing the existence of RRE and providing first-order methods for approximating RRE. Finally, we demonstrate the effectiveness of our approach in practice by building the corresponding generative adversarial policy neural network and using it to compute RRE in a variety of infinite-horizon Markov exchange economies.

cs.GT↗

arXiv2025

Efficient Inverse Multiagent Learning

In this paper, we study inverse game theory (resp. inverse multiagent learning) in which the goal is to find parameters of a game's payoff functions for which the expected (resp. sampled) behavior is an equilibrium. We formulate these problems as generative-adversarial (i.e., min-max) optimization problems, for which we develop polynomial-time algorithms to solve, the former of which relies on an exact first-order oracle, and the latter, a stochastic one. We extend our approach to solve inverse multiagent simulacral learning in polynomial time and number of samples. In these problems, we seek a simulacrum, meaning parameters and an associated equilibrium that replicate the given observations in expectation. We find that our approach outperforms the widely-used ARIMA method in predicting prices in Spanish electricity markets based on time-series data.

cs.GT↗

arXiv2025

Tractable General Equilibrium

We study Walrasian economies (or general equilibrium models) and their solution concept, the Walrasian equilibrium. A key challenge in this domain is identifying price-adjustment processes that converge to equilibrium. One such process, t\^atonnement, is an auction-like algorithm first proposed in 1874 by L\'eon Walras. While continuous-time variants of t\^atonnement are known to converge to equilibrium in economies satisfying the Weak Axiom of Revealed Preferences (WARP), the process fails to converge in a pathological Walrasian economy known as the Scarf economy. To address these issues, we analyze Walrasian economies using variational inequalities (VIs), an optimization framework. We introduce the class of mirror extragradient algorithms, which, under suitable Lipschitz-continuity-like assumptions, converge to a solution of any VI satisfying the Minty condition in polynomial time. We show that the set of Walrasian equilibria of any balanced economy-which includes among others Arrow-Debreu economies-corresponds to the solution set of an associated VI that satisfies the Minty condition but is generally discontinuous. Applying the mirror extragradient algorithm to this VI we obtain a class of t\^atonnement-like processes, which we call the mirror extrat\^atonnement process. While our VI formulation is generally discontinuous, it is Lipschitz-continuous in variationally stable Walrasian economies with bounded elasticity-including those satisfying WARP and the Scarf economy-thus establishing the polynomial-time convergence of mirror extrat\^atonnement in these economies. We validate our approach through experiments on large Arrow-Debreu economies with Cobb-Douglas, Leontief, and CES consumers, as well as the Scarf economy, demonstrating fast convergence in all cases without failure.

cs.GT↗

arXiv2025

Banzhaf Power in Hierarchical Voting Games

The Banzhaf Power Index (BPI) is a method of measuring the power of voters in determining the outcome of a voting game. Some voting games exhibit a hierarchical structure, including the US electoral college and ensemble learning methods; we call such games hierarchical voting games. It is generally understood that BPI in hierarchical voting games can be computed via a recursive decomposition of the hierarchy, which can substantially reduce the calculation's complexity. We identify a key (previously undocumented) assumption on which this decomposition is based, namely balance, meaning one group of voters has enough votes to win whenever the complementary group of voters does not, and vice versa. We then introduce a generalization of BPI that we call Extended BPI (EBPI) for all voting games, including those that are not balanced, which simplifies to BPI in balanced games. We show that BPI in unbalanced hierarchical voting games decomposes in terms of EBPI at each level in the hierarchy, which yields computational savings analogous to those achieved in the balanced case. As a sample application, we take advantage of the compositionality of language, and model the impact of individual words on a sentence's sentiment as a voting game. As the complement of a phrase in a sentence does not necessarily have the opposite sentiment, this voting game is unbalanced and requires our decomposition of BPI in terms of EBPI. Our results suggest that EBPI is an effective proxy for BPI (because the meaning of a sentence is not always 100\% compositional), and demonstrate a dramatic improvement in run time.

cs.GT↗

arXiv2025

A Unifying View of Linear Function Approximation in Off-Policy RL Through Matrix Splitting and Preconditioning

In off-policy policy evaluation (OPE) tasks within reinforcement learning, Temporal Difference Learning(TD) and Fitted Q-Iteration (FQI) have traditionally been viewed as differing in the number of updates toward the target value function: TD makes one update, FQI makes an infinite number, and Partial Fitted Q-Iteration (PFQI) performs a finite number. We show that this view is not accurate, and provide a new mathematical perspective under linear value function approximation that unifies these methods as a single iterative method solving the same linear system, but using different matrix splitting schemes and preconditioners. We show that increasing the number of updates under the same target value function, i.e., the target network technique, is a transition from using a constant preconditioner to using a data-feature adaptive preconditioner. This elucidates, for the first time, why TD convergence does not necessarily imply FQI convergence, and establishes tight convergence connections among TD, PFQI, and FQI. Our framework enables sharper theoretical results than previous work and characterization of the convergence conditions for each algorithm, without relying on assumptions about the features (e.g., linear independence). We also provide an encoder-decoder perspective to better understand the convergence conditions of TD, and prove, for the first time, that when a large learning rate doesn't work, trying a smaller one may help. Our framework also leads to the discovery of new crucial conditions on features for convergence, and shows how common assumptions about features influence convergence, e.g., the assumption of linearly independent features can be dropped without compromising the convergence guarantees of stochastic TD in the on-policy setting. This paper is also the first to introduce matrix splitting into the convergence analysis of these algorithms.

cs.LG↗

arXiv2024

Empirical Game-Theoretic Analysis: A Survey

In the empirical approach to game-theoretic analysis (EGTA), the model of the game comes not from declarative representation, but is derived by interrogation of a procedural description of the game environment. The motivation for developing this approach was to enable game-theoretic reasoning about strategic situations too complex for analytic specification and solution. Since its introduction over twenty years ago, EGTA has been applied to a wide range of multiagent domains, from auctions and markets to recreational games to cyber-security. We survey the extensive methodology developed for EGTA over the years, organized by the elemental subproblems comprising the EGTA process. We describe key EGTA concepts and techniques, and the questions at the frontier of EGTA research. Recent advances in machine learning have accelerated progress in EGTA, and promise to significantly expand our capacities for reasoning about complex game situations.

cs.GT↗

arXiv2024

Convex-Concave Zero-sum Markov Stackelberg Games

Zero-sum Markov Stackelberg games can be used to model myriad problems, in domains ranging from economics to human robot interaction. In this paper, we develop policy gradient methods that solve these games in continuous state and action settings using noisy gradient estimates computed from observed trajectories of play. When the games are convex-concave, we prove that our algorithms converge to Stackelberg equilibrium in polynomial time. We also show that reach-avoid problems are naturally modeled as convex-concave zero-sum Markov Stackelberg games, and that Stackelberg equilibrium policies are more effective than their Nash counterparts in these problems.

cs.GT↗

arXiv2023

T\^atonnement in Homothetic Fisher Markets

A prevalent theme in the economics and computation literature is to identify natural price-adjustment processes by which sellers and buyers in a market can discover equilibrium prices. An example of such a process is t\^atonnement, an auction-like algorithm first proposed in 1874 by French economist Walras in which sellers adjust prices based on the Marshallian demands of buyers. A dual concept in consumer theory is a buyer's Hicksian demand. In this paper, we identify the maximum of the absolute value of the elasticity of the Hicksian demand, as an economic parameter sufficient to capture and explain a range of convergent and non-convergent t\^atonnement behaviors in a broad class of markets. In particular, we prove the convergence of t\^atonnement at a rate of $O((1+\varepsilon^2)/T)$, in homothetic Fisher markets with bounded price elasticity of Hicksian demand, i.e., Fisher markets in which consumers have preferences represented by homogeneous utility functions and the price elasticity of their Hicksian demand is bounded, where $\varepsilon \geq 0$ is the maximum absolute value of the price elasticity of Hicksian demand across all buyers. Our result not only generalizes known convergence results for CES Fisher markets, but extends them to mixed nested CES markets and Fisher markets with continuous, possibly non-concave, homogeneous utility functions. Our convergence rate covers the full spectrum of nested CES utilities, including Leontief and linear utilities, unifying previously existing disparate convergence and non-convergence results. In particular, for $\varepsilon = 0$, i.e., Leontief markets, we recover the best-known convergence rate of $O(1/T)$, and as $\varepsilon \to \infty$, e.g., linear Fisher markets, we obtain non-convergent behavior, as expected.

cs.GT↗

arXiv2023

Fisher Markets with Social Influence

A Fisher market is an economic model of buyer and seller interactions in which each buyer's utility depends only on the bundle of goods she obtains. Many people's interests, however, are affected by their social interactions with others. In this paper, we introduce a generalization of Fisher markets, namely influence Fisher markets, which captures the impact of social influence on buyers' utilities. We show that competitive equilibria in influence Fisher markets correspond to generalized Nash equilibria in an associated pseudo-game, which implies the existence of competitive equilibria in all influence Fisher markets with continuous and concave utility functions. We then construct a monotone pseudo-game, whose variational equilibria and their duals together characterize competitive equilibria in influence Fisher markets with continuous, jointly concave, and homogeneous utility functions. This observation implies that competitive equilibria in these markets can be computed in polynomial time under standard smoothness assumptions on the utility functions. The dual of this second pseudo-game enables us to interpret the competitive equilibria of influence CCH Fisher markets as the solutions to a system of simultaneous Stackelberg games. Finally, we derive a novel first-order method that solves this Stackelberg system in polynomial time, prove that it is equivalent to computing competitive equilibrium prices via t\^{a}tonnement, and run experiments that confirm our theoretical results.

cs.GT↗

arXiv2022

Regret Pruning for Learning Equilibria in Simulation-Based Games

In recent years, empirical game-theoretic analysis (EGTA) has emerged as a powerful tool for analyzing games in which an exact specification of the utilities is unavailable. Instead, EGTA assumes access to an oracle, i.e., a simulator, which can generate unbiased noisy samples of players' unknown utilities, given a strategy profile. Utilities can thus be empirically estimated by repeatedly querying the simulator. Recently, various progressive sampling (PS) algorithms have been proposed, which aim to produce PAC-style learning guarantees (e.g., approximate Nash equilibria with high probability) using as few simulator queries as possible. One recent work introduces a pruning technique called regret-pruning which further minimizes the number of simulator queries placed in PS algorithms which aim to learn pure Nash equilibria. In this paper, we address a serious limitation of this original regret pruning approach -- it is only able to guarantee that true pure Nash equilibria of the empirical game are approximate equilibria of the true game, and is unable to provide any strong guarantees regarding the efficacy of approximate pure Nash equilibria. This is a significant limitation since in many games, pure Nash equilibria are computationally intractable to find, or even non-existent. We introduce three novel regret pruning variations. The first two variations generalize the original regret pruning approach to yield guarantees for approximate pure Nash equilibria of the empirical game. The third variation goes further to even yield strong guarantees for all approximate mixed Nash equilibria of the empirical game. We use these regret pruning variations to design two novel progressive sampling algorithms, PS-REG+ and PS-REG-M, which experimentally outperform the previous state-of-the-art algorithms for learning pure and mixed equilibria, respectively, of simulation-based games.

cs.GT↗

arXiv2022

Zero-Sum Stochastic Stackelberg Games

Zero-sum stochastic games have found important applications in a variety of fields, from machine learning to economics. Work on this model has primarily focused on the computation of Nash equilibrium due to its effectiveness in solving adversarial board and video games. Unfortunately, a Nash equilibrium is not guaranteed to exist in zero-sum stochastic games when the payoffs at each state are not convex-concave in the players' actions. A Stackelberg equilibrium, however, is guaranteed to exist. Consequently, in this paper, we study zero-sum stochastic Stackelberg games. Going beyond known existence results for (non-stationary) Stackelberg equilibria, we prove the existence of recursive (i.e., Markov perfect) Stackelberg equilibria (recSE) in these games, provide necessary and sufficient conditions for a policy profile to be a recSE, and show that recSE can be computed in (weakly) polynomial time via value iteration. Finally, we show that zero-sum stochastic Stackelberg games can model the problem of pricing and allocating goods across agents and time. More specifically, we propose a zero-sum stochastic Stackelberg game whose recSE correspond to the recursive competitive equilibria of a large class of stochastic Fisher markets. We close with a series of experiments that showcase how our methodology can be used to solve the consumption-savings problem in stochastic Fisher markets.

cs.GT↗