When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent population. Within such a process, the update rules of "who to compete with" (i.e., the opponent mixture) and "how to beat them" (i.e., finding best responses) are underpinned by manually developed game theoretical principles such as fictitious play and Double Oracle. In this paper we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the update rule without explicit human design. Specifically, we parameterise the opponent selection module by neural networks and the best-response module by optimisation subroutines, and update their parameters solely via interaction with the game engine, where both players aim to minimise their exploitability. Surprisingly, even without human design, the discovered MARL algorithms achieve competitive or even better performance with the state-of-the-art population-based game solvers (e.g., PSRO) on Games of Skill, differentiable Lotto, non-transitive Mixture Games, Iterated Matching Pennies, and Kuhn Poker. Additionally, we show that LMAC is able to generalise from small games to large games, for example training on Kuhn Poker and outperforming PSRO on Leduc Poker. Our work inspires a promising future direction to discover general MARL algorithms solely from data.

Policy Space Response Oracles (PSRO) is a deep reinforcement learning algorithm for two-player zero-sum games that has empirically found approximate Nash equilibria in large games. Although PSRO is guaranteed to converge to a Nash equilibrium, it may take an exponential number of iterations as the number of infostates grows. We propose Extensive-Form Double Oracle (XDO), an extensive-form double oracle algorithm that is guaranteed to converge to an approximate Nash equilibrium linearly in the number of infostates. Unlike PSRO, which mixes best responses at the root of the game, XDO mixes best responses at every infostate. We also introduce Neural XDO (NXDO), where the best response is learned through deep RL. In tabular experiments on Leduc poker, we find that XDO achieves an approximate Nash equilibrium in a number of iterations 1-2 orders of magnitude smaller than PSRO. In experiments on a modified Leduc poker game, we show that tabular XDO achieves over 11x lower exploitability than CFR and over 82x lower exploitability than PSRO and XFP in the same amount of time. We also show that NXDO beats PSRO and is competitive with NFSP on a large no-limit poker game.

A* search is an informed search algorithm that uses a heuristic function to guide the order in which nodes are expanded. Since the computation required to expand a node and compute the heuristic values for all of its generated children grows linearly with the size of the action space, A* search can become impractical for problems with large action spaces. This computational burden becomes even more apparent when heuristic functions are learned by general, but computationally expensive, deep neural networks. To address this problem, we introduce DeepCubeAQ, a deep reinforcement learning and search algorithm that builds on the DeepCubeA algorithm and deep Q-networks. DeepCubeAQ learns a heuristic function that, with a single forward pass through a deep neural network, computes the sum of the transition cost and the heuristic value of all of the children of a node without explicitly generating any of the children, eliminating the need for node expansions. DeepCubeAQ then uses a novel variant of A* search, called AQ* search, that uses the deep Q-network to guide search. We use DeepCubeAQ to solve the Rubik's cube when formulated with a large action space that includes 1872 meta-actions and show that this 157-fold increase in the size of the action space incurs less than a 4-fold increase in computation time when performing AQ* search and that AQ* search is orders of magnitude faster than A* search.

Finding approximate Nash equilibria in zero-sum imperfect-information games is challenging when the number of information states is large. Policy Space Response Oracles (PSRO) is a deep reinforcement learning algorithm grounded in game theory that is guaranteed to converge to an approximate Nash equilibrium. However, PSRO requires training a reinforcement learning policy at each iteration, making it too slow for large games. We show through counterexamples and experiments that DCH and Rectified PSRO, two existing approaches to scaling up PSRO, fail to converge even in small games. We introduce Pipeline PSRO (P2SRO), the first scalable general method for finding approximate Nash equilibria in large zero-sum imperfect-information games. P2SRO is able to parallelize PSRO with convergence guarantees by maintaining a hierarchical pipeline of reinforcement learning workers, each training against the policies generated by lower levels in the hierarchy. We show that unlike existing methods, P2SRO converges to an approximate Nash equilibrium, and does so faster as the number of parallel workers increases, across a variety of imperfect information games. We also introduce an open-source environment for Barrage Stratego, a variant of Stratego with an approximate game tree complexity of $10^{50}$. P2SRO is able to achieve state-of-the-art performance on Barrage Stratego and beats all existing bots.

Dealing with sparse rewards is a longstanding challenge in reinforcement learning. The recent use of hindsight methods have achieved success on a variety of sparse-reward tasks, but they fail on complex tasks such as stacking multiple blocks with a robot arm in simulation. Curiosity-driven exploration using the prediction error of a learned dynamics model as an intrinsic reward has been shown to be effective for exploring a number of sparse-reward environments. We present a method that combines hindsight with curiosity-driven exploration and curriculum learning in order to solve the challenging sparse-reward block stacking task. We are the first to stack more than two blocks using only sparse reward without human demonstrations.

A generally intelligent agent must be able to teach itself how to solve problems in complex domains with minimal human supervision. Recently, deep reinforcement learning algorithms combined with self-play have achieved superhuman proficiency in Go, Chess, and Shogi without human data or domain knowledge. In these environments, a reward is always received at the end of the game, however, for many combinatorial optimization environments, rewards are sparse and episodes are not guaranteed to terminate. We introduce Autodidactic Iteration: a novel reinforcement learning algorithm that is able to teach itself how to solve the Rubik's Cube with no human assistance. Our algorithm is able to solve 100% of randomly scrambled cubes while achieving a median solve length of 30 moves -- less than or equal to solvers that employ human domain knowledge.