Reevaluating Policy Gradient Methods for Imperfect-Information Games

In the past decade, motivated by the putative failure of naive self-play deep reinforcement learning (DRL) in adversarial imperfect-information games, researchers have developed numerous DRL algorithms based on fictitious play (FP), double oracle (DO), and counterfactual regret minimization (CFR). In light of recent results of the magnetic mirror descent algorithm, we hypothesize that simpler generic policy gradient methods like PPO are competitive with or superior to these FP, DO, and CFR-based DRL approaches. To facilitate the resolution of this hypothesis, we implement and release the first broadly accessible exact exploitability computations for four large games. Using these games, we conduct the largest-ever exploitability comparison of DRL algorithms for imperfect-information games. Over 5600 training runs, FP, DO, and CFR-based approaches fail to outperform generic policy gradient methods. Code is available at https://github.com/nathanlct/IIG-RL-Benchmark and https://github.com/gabrfarina/exp-a-spiel .

Neural Functional Transformers

The recent success of neural networks as implicit representation of data has driven growing interest in neural functionals: models that can process other neural networks as input by operating directly over their weight spaces. Nevertheless, constructing expressive and efficient neural functional architectures that can handle high-dimensional weight-space objects remains challenging. This paper uses the attention mechanism to define a novel set of permutation equivariant weight-space layers and composes them into deep equivariant models called neural functional Transformers (NFTs). NFTs respect weight-space permutation symmetries while incorporating the advantages of attention, which have exhibited remarkable success across multiple domains. In experiments processing the weights of feedforward MLPs and CNNs, we find that NFTs match or exceed the performance of prior weight-space methods. We also leverage NFTs to develop Inr2Array, a novel method for computing permutation invariant latent representations from the weights of implicit neural representations (INRs). Our proposed method improves INR classification accuracy by up to $+17\%$ over existing methods. We provide an implementation of our layers at https://github.com/AllanYangZhou/nfn.

The Update Equivalence Framework for Decision-Time Planning

The process of revising (or constructing) a policy immediately prior to execution -- known as decision-time planning -- is key to achieving superhuman performance in perfect-information settings like chess and Go. A recent line of work has extended decision-time planning to more general imperfect-information settings, leading to superhuman performance in poker. However, these methods requires considering subgames whose sizes grow quickly in the amount of non-public information, making them unhelpful when the amount of non-public information is large. Motivated by this issue, we introduce an alternative framework for decision-time planning that is not based on subgames but rather on the notion of update equivalence. In this framework, decision-time planning algorithms simulate updates of synchronous learning algorithms. This framework enables us to introduce a new family of principled decision-time planning algorithms that do not rely on public information, opening the door to sound and effective decision-time planning in settings with large amounts of non-public information. In experiments, members of this family produce comparable or superior results compared to state-of-the-art approaches in Hanabi and improve performance in 3x3 Abrupt Dark Hex and Phantom Tic-Tac-Toe.

Cheap Talk Discovery and Utilization in Multi-Agent Reinforcement Learning

By enabling agents to communicate, recent cooperative multi-agent reinforcement learning (MARL) methods have demonstrated better task performance and more coordinated behavior. Most existing approaches facilitate inter-agent communication by allowing agents to send messages to each other through free communication channels, i.e., cheap talk channels. Current methods require these channels to be constantly accessible and known to the agents a priori. In this work, we lift these requirements such that the agents must discover the cheap talk channels and learn how to use them. Hence, the problem has two main parts: cheap talk discovery (CTD) and cheap talk utilization (CTU). We introduce a novel conceptual framework for both parts and develop a new algorithm based on mutual information maximization that outperforms existing algorithms in CTD/CTU settings. We also release a novel benchmark suite to stimulate future research in CTD/CTU.

Permutation Equivariant Neural Functionals

This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned optimization, processing implicit neural representations, network editing, and policy evaluation, there are few unifying principles for designing effective architectures that process the weights of other networks. We approach the design of neural functionals through the lens of symmetry, in particular by focusing on the permutation symmetries that arise in the weights of deep feedforward networks because hidden layer neurons have no inherent order. We introduce a framework for building permutation equivariant neural functionals, whose architectures encode these symmetries as an inductive bias. The key building blocks of this framework are NF-Layers (neural functional layers) that we constrain to be permutation equivariant through an appropriate parameter sharing scheme. In our experiments, we find that permutation equivariant neural functionals are effective on a diverse set of tasks that require processing the weights of MLPs and CNNs, such as predicting classifier generalization, producing "winning ticket" sparsity masks for initializations, and editing the weights of implicit neural representations (INRs). In addition, we provide code for our models and experiments at https://github.com/AllanYangZhou/nfn.

Abstracting Imperfect Information Away from Two-Player Zero-Sum Games

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and decision-time planning algorithms for common-payoff games. Unfortunately, a naive application of the same insight to two-player zero-sum games fails because Nash equilibria of the game with public policy announcements may not correspond to Nash equilibria of the original game. As a consequence, existing sound decision-time planning algorithms require complicated additional mechanisms that have unappealing properties. The main contribution of this work is showing that certain regularized equilibria do not possess the aforementioned non-correspondence problem -- thus, computing them can be treated as perfect information problems. Because these regularized equilibria can be made arbitrarily close to Nash equilibria, our result opens the door to a new perspective on solving two-player zero-sum games and, in particular, yields a simplified framework for decision-time planning in two-player zero-sum games, void of the unappealing properties that plague existing decision-time planning approaches.

Perfectly Secure Steganography Using Minimum Entropy Coupling

Steganography is the practice of encoding secret information into innocuous content in such a manner that an adversarial third party would not realize that there is hidden meaning. While this problem has classically been studied in security literature, recent advances in generative models have led to a shared interest among security and machine learning researchers in developing scalable steganography techniques. In this work, we show that a steganography procedure is perfectly secure under \citet{cachin_perfect}'s information theoretic-model of steganography if and only if it is induced by a coupling. Furthermore, we show that, among perfectly secure procedures, a procedure is maximally efficient if and only if it is induced by a minimum entropy coupling. These insights yield what are, to the best of our knowledge, the first steganography algorithms to achieve perfect security guarantees with non-trivial efficiency; additionally, these algorithms are highly scalable. To provide empirical validation, we compare a minimum entropy coupling-based approach to three modern baselines -- arithmetic coding, Meteor, and adaptive dynamic grouping -- using GPT-2 and WaveRNN as communication channels. We find that the minimum entropy coupling-based approach yields superior encoding efficiency, despite its stronger security constraints. In aggregate, these results suggest that it may be natural to view information-theoretic steganography through the lens of minimum entropy coupling.

A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Games

Algorithms designed for single-agent reinforcement learning (RL) generally fail to converge to equilibria in two-player zero-sum (2p0s) games. Conversely, game-theoretic algorithms for approximating Nash and quantal response equilibria (QREs) in 2p0s games are not typically competitive for RL and can be difficult to scale. As a result, algorithms for these two cases are generally developed and evaluated separately. In this work, we show that a single algorithm -- a simple extension to mirror descent with proximal regularization that we call magnetic mirror descent (MMD) -- can produce strong results in both settings, despite their fundamental differences. From a theoretical standpoint, we prove that MMD converges linearly to QREs in extensive-form games -- this is the first time linear convergence has been proven for a first order solver. Moreover, applied as a tabular Nash equilibrium solver via self-play, we show empirically that MMD produces results competitive with CFR in both normal-form and extensive-form games with full feedback (this is the first time that a standard RL algorithm has done so) and also that MMD empirically converges in black-box feedback settings. Furthermore, for single-agent deep RL, on a small collection of Atari and Mujoco games, we show that MMD can produce results competitive with those of PPO. Lastly, for multi-agent deep RL, we show MMD can outperform NFSP in 3x3 Abrupt Dark Hex.

Learning to Coordinate with Humans using Action Features

An unaddressed challenge in human-AI coordination is to enable AI agents to exploit the semantic relationships between the features of actions and the features of observations. Humans take advantage of these relationships in highly intuitive ways. For instance, in the absence of a shared language, we might point to the object we desire or hold up our fingers to indicate how many objects we want. To address this challenge, we investigate the effect of network architecture on the propensity of learning algorithms to exploit these semantic relationships. Across a procedurally generated coordination task, we find that attention-based architectures that jointly process a featurized representation of observations and actions have a better inductive bias for zero-shot coordination. Through fine-grained evaluation and scenario analysis, we show that the resulting policies are human-interpretable. Moreover, such agents coordinate with people without training on any human data.

Implicit Communication as Minimum Entropy Coupling

In many common-payoff games, achieving good performance requires players to develop protocols for communicating their private information implicitly -- i.e., using actions that have non-communicative effects on the environment. Multi-agent reinforcement learning practitioners typically approach this problem using independent learning methods in the hope that agents will learn implicit communication as a byproduct of expected return maximization. Unfortunately, independent learning methods are incapable of doing this in many settings. In this work, we isolate the implicit communication problem by identifying a class of partially observable common-payoff games, which we call implicit referential games, whose difficulty can be attributed to implicit communication. Next, we introduce a principled method based on minimum entropy coupling that leverages the structure of implicit referential games, yielding a new perspective on implicit communication. Lastly, we show that this method can discover performant implicit communication protocols in settings with very large spaces of messages.