The centralized training for decentralized execution paradigm emerged as the state-of-the-art approach to ϵ-optimally solving decentralized partially observable Markov decision processes. However, scalability remains a significant issue. This paper presents a novel and more scalable alternative, namely the sequential-move centralized training for decentralized execution. This paradigm further pushes the applicability of the Bellman’s principle of optimality, raising three new properties. First, it allows a central planner to reason upon sufficient sequential-move statistics instead of prior simultaneous-move ones. Next, it proves that ϵ-optimal value functions are piecewise linear and convex in such sufficient sequential-move statistics. Finally, it drops the complexity of the backup operators from double exponential to polynomial at the expense of longer planning horizons. Besides, it makes it easy to use single-agent methods, e.g., SARSA algorithm enhanced with these findings, while still preserving convergence guarantees. Experiments on two- as well as many-agent domains from the literature against ϵ-optimal simultaneous-move solvers confirm the superiority of our novel approach. This paradigm opens the door for efficient planning and reinforcement learning methods for multi-agent systems.

A recent theory shows that a multi-player decentralized partially observable Markov decision process can be transformed into an equivalent single-player game, enabling the application of Bellman's principle of optimality to solve the single-player game by breaking it down into single-stage subgames. However, this approach entangles the decision variables of all players at each single-stage subgame, resulting in backups with a double-exponential complexity. This paper demonstrates how to disentangle these decision variables while maintaining optimality under hierarchical information sharing, a prominent management style in our society. To achieve this, we apply the principle of optimality to solve any single-stage subgame by breaking it down further into smaller subgames, enabling us to make single-player decisions at a time. Our approach reveals that extensive-form games always exist with solutions to a single-stage subgame, significantly reducing time complexity. Our experimental results show that the algorithms leveraging these findings can scale up to much larger multi-player games without compromising optimality.

min-max optimization problems recently arose in various settings. From Generative Adversarial Networks (GANs) to aerodynamic optimization through Game Theory, the assumptions on the objective function vary. Motivated by the applications to deep learning and especially GANs, most recent works assume differentiability to design local search algorithms such as Gradient Descend Ascent (GDA). In contrast, this work will only require $\alpha -$Hölder properties to tackle general game-theoretic problems with poor continuity assumptions. Focusing on the example of problems in which max and min optimization variables live in simplices, we provide a simple algorithm, based on Deterministic Optimistic Optimization (DOO), relying on an outer min-optimization using the solutions of an inner max-optimization. The algorithm is shown to converge in finite time to an -global optimum. Experimental validations are given and the time complexity of our algorithm is studied.