Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite nonlinearity and non-convexity introduced by the implicit representation. Furthermore, we derive convergence rates for both cases which allow us to identify conditions under which stochastic gradient descent (SGD) with this implicit representation converges substantially faster than its explicit counterpart. Finally, we provide empirical results in some simple domains that illustrate the theoretical findings.

We introduce a new approach for computing optimal equilibria and mechanisms via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated, communication, and certification equilibria. We observe that optimal equilibria are minimax equilibrium strategies of a player in an extensiveform zero-sum game. This reformulation allows us to apply techniques for learning in zero-sum games, yielding the first learning dynamics that converge to optimal equilibria, not only in empirical averages, but also in iterates. We demonstrate the practical scalability and flexibility of our approach by attaining state-of-the-art performance in benchmark tabular games, and by computing an optimal mechanism for a sequential auction design problem using deep reinforcement learning.

Despite the success of cooperative multi-agent reinforcement learning algorithms, most of them focus on a single team composition, which prevents them from being used in more realistic scenarios where dynamic team composition is possible. While some studies attempt to solve this problem via multi-task learning in a fixed set of team compositions, there is still a risk of overfitting to the training set, which may lead to catastrophic performance when facing dramatically varying team compositions during execution. To address this problem, we propose to use mutual information (MI) as an augmented reward to prevent individual policies from relying too much on team-related information and encourage agents to learn policies that are robust in different team compositions. Optimizing this MI-augmented objective in an off-policy manner can be intractable due to the existence of dynamic marginal distribution. To alleviate this problem, we first propose a multi-agent policy iteration algorithm with a fixed marginal distribution and prove its convergence and optimality. Then, we propose to employ the Blahut-Arimoto algorithm and an imaginary team composition distribution for optimization with approximate marginal distribution as the practical implementation. Empirically, our method demonstrates strong zero-shot generalization to dynamic team compositions in complex cooperative tasks.

We show that Deep Neural Networks introduce two heteroscedastic Gumbel noise sources into Q-Learning. To account for these noise sources, we propose Double Gumbel Q-Learning, a Deep Q-Learning algorithm applicable for both discrete and continuous control. In discrete control, we derive a closed-form expression for the loss function of our algorithm. In continuous control, this loss function is intractable and we therefore derive an approximation with a hyperparameter whose value regulates pessimism in Q-Learning. We present a default value for our pessimism hyperparameter that enables DoubleGum to outperform DDPG, TD3, SAC, XQL, quantile regression, and Mixture-of-Gaussian Critics in aggregate over 33 tasks from DeepMind Control, MuJoCo, MetaWorld, and Box2D and show that tuning this hyperparameter may further improve sample efficiency.

Lewis signaling games are a class of simple communication games for simulating the emergence of language. In these games, two agents must agree on a communication protocol in order to solve a cooperative task. Previous work has shown that agents trained to play this game with reinforcement learning tend to develop languages that display undesirable properties from a linguistic point of view (lack of generalization, lack of compositionality, etc). In this paper, we aim to provide better understanding of this phenomenon by analytically studying the learning problem in Lewis games. As a core contribution, we demonstrate that the standard objective in Lewis games can be decomposed in two components: a co-adaptation loss and an information loss. This decomposition enables us to surface two potential sources of overfitting, which we show may undermine the emergence of a structured communication protocol. In particular, when we control for overfitting on the co-adaptation loss, we recover desired properties in the emergent languages: they are more compositional and generalize better.