One of the main challenges in offline Reinforcement Learning (RL) is the distribution shift that arises from the learned policy deviating from the data collection policy. This is often addressed by avoiding out-of-distribution (OOD) actions during policy improvement as their presence can lead to substantial performance degradation. This challenge is amplified in the offline Multi-Agent RL (MARL) setting since the joint action space grows exponentially with the number of agents. To avoid this curse of dimensionality, existing MARL methods adopt either value decomposition methods or fully decentralized training of individual agents. However, even when combined with standard conservatism principles, these methods can still result in the selection of OOD joint actions in offline MARL. To this end, we introduce AlberDICE, an offline MARL algorithm that alternatively performs centralized training of individual agents based on stationary distribution optimization. AlberDICE circumvents the exponential complexity of MARL by computing the best response of one agent at a time while effectively avoiding OOD joint action selection. Theoretically, we show that the alternating optimization procedure converges to Nash policies. In the experiments, we demonstrate that AlberDICE significantly outperforms baseline algorithms on a standard suite of MARL benchmarks.

The literature for the geometric properties of Riemannian Manifolds is immense and hence we cannot hope to survey them here; for an appetizer, we refer the reader to Burago et al. [93] and Lee [94] and references therein. On the other hand, as stated, it is not until recently that the long-run non-asymptotic behavior of optimization algorithms in Riemannian manifolds (even the smooth ones) has encountered a lot of interest. For concision, we have deferred here a detailed exposition of the rest of recent results to Appendix A of the paper's supplement. Additionally, in Appendix B we also give a bunch of motivating examples which can be solved by Riemannian min-max optimization. Many application problems can be formulated as the minimization or maximization of a smooth function over Riemannian manifold and has triggered a line of research on the extension of the classical first-order and second-order methods to Riemannian setting with asymptotic convergence to first-order stationary points in general [95].

Theorem, 4.2 - Optimizing Neural Nets.SupposeJ (', )is 1s-stronglysmoothinl1 norm. Let n bethe Sinkhornplanbetweenˆµand ˆ atregularization , andletD: = diam (X).

In Euclidean space, OCO boasts a robust theoretical foundation and numerous real-world applications, such as online load balancing (Molinaro, 2017), optimal control (Li et al., 2019), revenue maximization (Lin et al., 2019), and portfolio management (Jézéquel et al., 2022).

We establish upper bounds on the regrets of the problem with respect to time horizon, manifold curvature, and manifold dimension.

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