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Most of the literature on learning in games has focused on the restrictive setting where the underlying repeated game does not change over time. Much less is known about the convergence of no-regret learning algorithms in dynamic multiagent settings. In this paper, we characterize the convergence of optimistic gradient descent (OGD) in time-varying games. Our framework yields sharp convergence bounds for the equilibrium gap of OGD in zero-sum games parameterized on natural variation measures of the sequence of games, subsuming known results for static games. Furthermore, we establish improved second-order variation bounds under strong convexity-concavity, as long as each game is repeated multiple times. Our results also extend to time-varying general-sum multi-player games via a bilinear formulation of correlated equilibria, which has novel implications for meta-learning and for obtaining refined variation-dependent regret bounds, addressing questions left open in prior papers. Finally, we leverage our framework to also provide new insights on dynamic regret guarantees in static games. 1
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This content will become publicly available on April 1, 2025
Multi-Agent Meta-Reinforcement Learning: Sharper Convergence Rates with Task Similarity
Multi-agent reinforcement learning (MARL) has primarily focused on solving a single task in isolation, while in practice the environment is often evolving, leaving many related tasks to be solved. In this paper, we investigate the benefits of meta-learning in solving multiple MARL tasks collectively. We establish the first line of theoretical results for meta-learning in a wide range of fundamental MARL settings, including learning Nash equilibria in two-player zero-sum Markov games and Markov potential games, as well as learning coarse correlated equilibria in general-sum Markov games. Under natural notions of task similarity, we show that meta-learning achieves provable sharper convergence to various game-theoretical solution concepts than learning each task separately. As an important intermediate step, we develop multiple MARL algorithms with initialization-dependent convergence guarantees. Such algorithms integrate optimistic policy mirror descents with stage-based value updates, and their refined convergence guarantees (nearly) recover the best known results even when a good initialization is unknown. To our best knowledge, such results are also new and might be of independent interest. We further provide numerical simulations to corroborate our theoretical findings.
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- Award ID(s):
- 2029049
- PAR ID:
- 10546464
- Editor(s):
- Oh, A; Naumann, T; Globerson, A; Saenko, K; Hardt, M; Levine, S
- Publisher / Repository:
- NeurIPS
- Date Published:
- Edition / Version:
- 1
- Volume:
- 1
- Issue:
- 1
- ISBN:
- 9781713899921
- Subject(s) / Keyword(s):
- multi-agent reinforcement learning, convergence, meta-learning
- Format(s):
- Medium: X Size: 284 kb Other: pdf
- Size(s):
- 284 kb
- Location:
- New Orleans, LA
- Sponsoring Org:
- National Science Foundation
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