arXiv subjects

Zachary Roch

Publications and source records attributed to Zachary Roch.

3 recordsLinked to original sources

arXiv2025

Distributionally Robust Markov Games with Average Reward

We propose and study distributionally robust Markov games (DR-MGs) with the average-reward criterion as a crucial framework for multi-agent decision-making under model mismatches and over extended horizons. Under a standard irreducible assumption, we first derive a correspondence between the optimal policies and the solutions of the robust Bellman equation, based on which we further show the existence of a stationary Nash Equilibrium (NE) of the game. We further study DR-MGs under a more general weakly communicating setting. We construct a set-valued map based on the constant-gain optimal robust Bellman operator and show that its value is a subset of the best-response policies. We further prove that this map admits a fixed point, which implies the existence of NE. We then design two algorithms, Robust Nash-Iteration and robust TD Descent, with provably convergent guarantees. Finally, we show that the NE under average-reward can be approximated by the ones for the discounted DR-MGs as the discount factor approaches one. Our studies provide a comprehensive theoretical and algorithmic foundation for decision-making in complex, uncertain, and long-running multi-player environments.

cs.MA↗

arXiv2025

Model-Free Robust Average-Reward Reinforcement Learning with Sample Complexity Analysis

Robust reinforcement learning (RL) under the average-reward criterion is essential for long-term decision-making, particularly when the environment may differ from its training dynamics. However, most existing studies focus on model-based settings and provide only asymptotic guarantees, hindering their principled understanding and practical deployment, especially in data-limited scenarios. We aim to close this gap by proposing a model-free algorithm, \textbf{Robust Halpern Iteration (RHI)}. We first design our algorithm based on a black-box sampling oracle, which can estimate the worst-case performance accurately. We then derive the finite sample complexity of RHI under the generative model setting, assuming the sampling oracle. To concretely design such an oracle, we propose a $K$-order multi-level Monte-Carlo estimator, which is shown to have a lower bias compared to prior methods. We further instantiate our design for multiple uncertainty models, including KL and $\chi^2$ divergence sets, and show that our RHI algorithm achieves an $\varepsilon$-optimal robust policy with a sample complexity of $\tilde{\mathcal{O}}\left( \frac{SA\mathcal{H}^2}{\varepsilon^{(2+o(1))}}\right)$, where $S,A$ are the number of states and actions, and $\mathcal{H}$ is the robust optimal span. Our result asymptotically matches the best complexity in robust average reward RL.

cs.LG↗

arXiv2024

Blockchain Services for Digital Government: An Exploration of NFT Applications in the Metaverse

The full implementation of the metaverse requires the integration of the physical and digital worlds. Applications built on Distributed Ledger Technology (DLT) hold the power to move society closer towards the ideal metaverse through innovations like Non-Fungible Tokens (NFTs). Due to a combination of the infancy of this technology and the significant implications it holds in the public and private sectors, adoption across both sectors is currently limited. To foster the creation of sustainable smart cities built on this technology, education on how this technology may function in an integrated metaverse is paramount. This is due to the necessary compatibility across industries needed between public and private data. As certain industries are more regulated than others, such as finance or healthcare, a robust system is needed to allow for varying degrees of freedom. This chapter illustrates numerous facets of this conceptual framework.

cs.CR↗