32 research outputs found
Approximate dynamic programming for two-player zero-sum Markov games
International audienceThis paper provides an analysis of error propagation in Approximate Dynamic Programming applied to zero-sum two-player Stochastic Games. We provide a novel and unified error propagation analysis in L p-norm of three well-known algorithms adapted to Stochastic Games (namely Approximate Value Iteration, Approximate Policy Iteration and Approximate Generalized Policy Iteratio,n). We show that we can achieve a stationary policy which is 2γ+ (1−γ) 2-optimal, where is the value function approximation error and is the approximate greedy operator error. In addition , we provide a practical algorithm (AGPI-Q) to solve infinite horizon γ-discounted two-player zero-sum Stochastic Games in a batch setting. It is an extension of the Fitted-Q algorithm (which solves Markov Decisions Processes from data) and can be non-parametric. Finally, we demonstrate experimentally the performance of AGPI-Q on a simultaneous two-player game, namely Alesia
Open-ended Learning in Symmetric Zero-sum Games
Zero-sum games such as chess and poker are, abstractly, functions that
evaluate pairs of agents, for example labeling them `winner' and `loser'. If
the game is approximately transitive, then self-play generates sequences of
agents of increasing strength. However, nontransitive games, such as
rock-paper-scissors, can exhibit strategic cycles, and there is no longer a
clear objective -- we want agents to increase in strength, but against whom is
unclear. In this paper, we introduce a geometric framework for formulating
agent objectives in zero-sum games, in order to construct adaptive sequences of
objectives that yield open-ended learning. The framework allows us to reason
about population performance in nontransitive games, and enables the
development of a new algorithm (rectified Nash response, PSRO_rN) that uses
game-theoretic niching to construct diverse populations of effective agents,
producing a stronger set of agents than existing algorithms. We apply PSRO_rN
to two highly nontransitive resource allocation games and find that PSRO_rN
consistently outperforms the existing alternatives.Comment: ICML 2019, final versio
A Generalised Method for Empirical Game Theoretic Analysis
This paper provides theoretical bounds for empirical game theoretical
analysis of complex multi-agent interactions. We provide insights in the
empirical meta game showing that a Nash equilibrium of the meta-game is an
approximate Nash equilibrium of the true underlying game. We investigate and
show how many data samples are required to obtain a close enough approximation
of the underlying game. Additionally, we extend the meta-game analysis
methodology to asymmetric games. The state-of-the-art has only considered
empirical games in which agents have access to the same strategy sets and the
payoff structure is symmetric, implying that agents are interchangeable.
Finally, we carry out an empirical illustration of the generalised method in
several domains, illustrating the theory and evolutionary dynamics of several
versions of the AlphaGo algorithm (symmetric), the dynamics of the Colonel
Blotto game played by human players on Facebook (symmetric), and an example of
a meta-game in Leduc Poker (asymmetric), generated by the PSRO multi-agent
learning algorithm.Comment: will appear at AAMAS'1
A multi-agent reinforcement learning model of common-pool resource appropriation
Humanity faces numerous problems of common-pool resource appropriation. This class of multi-agent social dilemma includes the problems of ensuring sustainable use of fresh water, common fisheries, grazing pastures, and irrigation systems. Abstract models of common-pool resource appropriation based on non-cooperative game theory predict that self-interested agents will generally fail to find socially positive equilibria---a phenomenon called the tragedy of the commons. However, in reality, human societies are sometimes able to discover and implement stable cooperative solutions. Decades of behavioral game theory research have sought to uncover aspects of human behavior that make this possible. Most of that work was based on laboratory experiments where participants only make a single choice: how much to appropriate. Recognizing the importance of spatial and temporal resource dynamics, a recent trend has been toward experiments in more complex real-time video game-like environments. However, standard methods of non-cooperative game theory can no longer be used to generate predictions for this case. Here we show that deep reinforcement learning can be used instead. To that end, we study the emergent behavior of groups of independently learning agents in a partially observed Markov game modeling common-pool resource appropriation. Our experiments highlight the importance of trial-and-error learning in common-pool resource appropriation and shed light on the relationship between exclusion, sustainability, and inequality
Re-evaluating Evaluation
Progress in machine learning is measured by careful evaluation on problems of
outstanding common interest. However, the proliferation of benchmark suites and
environments, adversarial attacks, and other complications has diluted the
basic evaluation model by overwhelming researchers with choices. Deliberate or
accidental cherry picking is increasingly likely, and designing well-balanced
evaluation suites requires increasing effort. In this paper we take a step back
and propose Nash averaging. The approach builds on a detailed analysis of the
algebraic structure of evaluation in two basic scenarios: agent-vs-agent and
agent-vs-task. The key strength of Nash averaging is that it automatically
adapts to redundancies in evaluation data, so that results are not biased by
the incorporation of easy tasks or weak agents. Nash averaging thus encourages
maximally inclusive evaluation -- since there is no harm (computational cost
aside) from including all available tasks and agents.Comment: NIPS 2018, final versio
Scaling up Mean Field Games with Online Mirror Descent
We address scaling up equilibrium computation in Mean Field Games (MFGs)
using Online Mirror Descent (OMD). We show that continuous-time OMD provably
converges to a Nash equilibrium under a natural and well-motivated set of
monotonicity assumptions. This theoretical result nicely extends to
multi-population games and to settings involving common noise. A thorough
experimental investigation on various single and multi-population MFGs shows
that OMD outperforms traditional algorithms such as Fictitious Play (FP). We
empirically show that OMD scales up and converges significantly faster than FP
by solving, for the first time to our knowledge, examples of MFGs with hundreds
of billions states. This study establishes the state-of-the-art for learning in
large-scale multi-agent and multi-population games