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Paul Friedrich, Yulun Zhang, Michael Curry, Ludwig Dierks, Stephen McAleer, Jiaoyang Li, Tuomas Sandholm, Sven Seuken

Multi-Agent Path Finding (MAPF) involves determining paths for multiple agents to travel simultaneously through a shared area toward particular goal locations. This problem is computationally complex, especially when dealing with large numbers of agents, as is common in realistic applications like autonomous vehicle coordination. Finding an optimal solution is often computationally infeasible, making the use of approximate algorithms essential. Adding to the complexity, agents might act in a self-interested and strategic way, possibly misrepresenting their goals to the MAPF algorithm if it benefits them. Although the field of mechanism design offers tools to align incentives, using these tools without careful consideration can fail when only having access to approximately optimal outcomes. Since approximations are crucial for scalable MAPF algorithms, this poses a significant challenge. In this work, we introduce the problem of scalable mechanism design for MAPF and propose three strategyproof mechanisms, two of which even use approximate MAPF algorithms. We test our mechanisms on realistic MAPF domains with problem sizes ranging from dozens to hundreds of agents. Our findings indicate that they improve welfare beyond a simple baseline.

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Ioannis Anagnostides, Ioannis Panageas, Gabriele Farina, Tuomas Sandholm

Policy gradient methods enjoy strong practical performance in numerous tasks in reinforcement learning. Their theoretical understanding in multiagent settings, however, remains limited, especially beyond two-player competitive and potential Markov games. In this paper, we develop a new framework to characterize optimistic policy gradient methods in multi-player Markov games with a single controller. Specifically, under the further assumption that the game exhibits an equilibrium collapse, in that the marginals of coarse correlated equilibria (CCE) induce Nash equilibria (NE), we show convergence to stationary $\epsilon$-NE in $O(1/\epsilon^2)$ iterations, where $O(\cdot)$ suppresses polynomial factors in the natural parameters of the game. Such an equilibrium collapse is well-known to manifest itself in two-player zero-sum Markov games, but also occurs even in a class of multi-player Markov games with separable interactions, as established by recent work. As a result, we bypass known complexity barriers for computing stationary NE when either of our assumptions fails. Our approach relies on a natural generalization of the classical Minty property that we introduce, which we anticipate to have further applications beyond Markov games.

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Ted Moskovitz, Aaditya K. Singh, DJ Strouse, Tuomas Sandholm, Ruslan Salakhutdinov, Anca D. Dragan, Stephen McAleer

Large language models are typically aligned with human preferences by optimizing $\textit{reward models}$ (RMs) fitted to human feedback. However, human preferences are multi-faceted, and it is increasingly common to derive reward from a composition of simpler reward models which each capture a different aspect of language quality. This itself presents a challenge, as it is difficult to appropriately weight these component RMs when combining them. Compounding this difficulty, because any RM is only a proxy for human evaluation, this process is vulnerable to $\textit{overoptimization}$, wherein past a certain point, accumulating higher reward is associated with worse human ratings. In this paper, we perform, to our knowledge, the first study on overoptimization in composite RMs, showing that correlation between component RMs has a significant effect on the locations of these points. We then introduce an approach to solve this issue using constrained reinforcement learning as a means of preventing the agent from exceeding each RM's threshold of usefulness. Our method addresses the problem of weighting component RMs by learning dynamic weights, naturally expressed by Lagrange multipliers. As a result, each RM stays within the range at which it is an effective proxy, improving evaluation performance. Finally, we introduce an adaptive method using gradient-free optimization to identify and optimize towards these points during a single run.

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Carlos Martin, Tuomas Sandholm

We propose a new method, called PiZero, that gives an agent the ability to plan in an abstract search space of its own creation that is completely decoupled from the real environment. Unlike prior approaches, this enables the agent to perform high-level planning at arbitrary timescales and reason in terms of compound or temporally-extended actions, which can be useful in environments where large numbers of base-level micro-actions are needed to perform relevant macro-actions. In addition, our method is more general than comparable prior methods because it handles settings with continuous action spaces and partial observability. We evaluate our method on multiple domains, including navigation tasks and Sokoban. Experimentally, it outperforms comparable prior methods without assuming access to an environment simulator.

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Yongyuan Liang, Yanchao Sun, Ruijie Zheng, Xiangyu Liu, Tuomas Sandholm, Furong Huang, Stephen McAleer

Robust reinforcement learning (RL) seeks to train policies that can perform well under environment perturbations or adversarial attacks. Existing approaches typically assume that the space of possible perturbations remains the same across timesteps. However, in many settings, the space of possible perturbations at a given timestep depends on past perturbations. We formally introduce temporally-coupled perturbations, presenting a novel challenge for existing robust RL methods. To tackle this challenge, we propose GRAD, a novel game-theoretic approach that treats the temporally-coupled robust RL problem as a partially-observable two-player zero-sum game. By finding an approximate equilibrium in this game, GRAD ensures the agent's robustness against temporally-coupled perturbations. Empirical experiments on a variety of continuous control tasks demonstrate that our proposed approach exhibits significant robustness advantages compared to baselines against both standard and temporally-coupled attacks, in both state and action spaces.

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Ioannis Anagnostides, Ioannis Panageas, Gabriele Farina, Tuomas Sandholm

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 \emph{optimistic gradient descent (OGD)} in time-varying games by drawing a strong connection with \emph{dynamic regret}. Our framework yields sharp convergence bounds for the equilibrium gap of OGD in zero-sum games parameterized on the \emph{minimal} first-order variation of the Nash equilibria and the second-order variation of the payoff matrices, subsuming known results for static games. Furthermore, we establish improved \emph{second-order} variation bounds under strong convexity-concavity, as long as each game is repeated multiple times. Our results also apply to time-varying \emph{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.

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Carlos Martin, Tuomas Sandholm

In this paper, we study the problem of computing an approximate Nash equilibrium of a continuous game. Such games naturally model many situations involving space, time, money, and other fine-grained resources or quantities. The standard measure of the closeness of a strategy profile to Nash equilibrium is exploitability, which measures how much utility players can gain from changing their strategy unilaterally. We introduce a new equilibrium-finding method that minimizes an approximation of the exploitability. This approximation employs a best-response ensemble for each player that maintains multiple candidate best responses for that player. In each iteration, the best-performing element of each ensemble is used in a gradient-based scheme to update the current strategy profile. The strategy profile and best-response ensembles are simultaneously trained to minimize and maximize the approximate exploitability, respectively. Experiments on a suite of benchmark games show that it outperforms previous methods.

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Carlos Martin, Tuomas Sandholm

We study the problem of computing an approximate Nash equilibrium of continuous-action game without access to gradients. Such game access is common in reinforcement learning settings, where the environment is typically treated as a black box. To tackle this problem, we apply zeroth-order optimization techniques that combine smoothed gradient estimators with equilibrium-finding dynamics. We model players' strategies using artificial neural networks. In particular, we use randomized policy networks to model mixed strategies. These take noise in addition to an observation as input and can flexibly represent arbitrary observation-dependent, continuous-action distributions. Being able to model such mixed strategies is crucial for tackling continuous-action games that lack pure-strategy equilibria. We evaluate the performance of our method using an approximation of the Nash convergence metric from game theory, which measures how much players can benefit from unilaterally changing their strategy. We apply our method to continuous Colonel Blotto games, single-item and multi-item auctions, and a visibility game. The experiments show that our method can quickly find high-quality approximate equilibria. Furthermore, they show that the dimensionality of the input noise is crucial for performance. To our knowledge, this paper is the first to solve general continuous-action games with unrestricted mixed strategies and without any gradient information.

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Ioannis Anagnostides, Gabriele Farina, Tuomas Sandholm

In this paper, we establish efficient and uncoupled learning dynamics so that, when employed by all players in multiplayer perfect-recall imperfect-information extensive-form games, the \emph{trigger regret} of each player grows as $O(\log T)$ after $T$ repetitions of play. This improves exponentially over the prior best known trigger-regret bound of $O(T^{1/4})$, and settles a recent open question by Bai et al. (2022). As an immediate consequence, we guarantee convergence to the set of \emph{extensive-form correlated equilibria} and \emph{coarse correlated equilibria} at a near-optimal rate of $\frac{\log T}{T}$. Building on prior work, at the heart of our construction lies a more general result regarding fixed points deriving from rational functions with \emph{polynomial degree}, a property that we establish for the fixed points of \emph{(coarse) trigger deviation functions}. Moreover, our construction leverages a refined \textit{regret circuit} for the convex hull, which -- unlike prior guarantees -- preserves the \emph{RVU property} introduced by Syrgkanis et al. (NIPS, 2015); this observation has an independent interest in establishing near-optimal regret under learning dynamics based on a CFR-type decomposition of the regret.

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