No Regrets: Investigating and Improving Regret Approximations for Curriculum Discovery

What data or environments to use for training to improve downstream performance is a longstanding and very topical question in reinforcement learning. In particular, Unsupervised Environment Design (UED) methods have gained recent attention as their adaptive curricula enable agents to be robust to in- and out-of-distribution tasks. We ask to what extent these methods are themselves robust when applied to a novel setting, closely inspired by a real-world robotics problem. Surprisingly, we find that the state-of-the-art UED methods either do not improve upon the na\"{i}ve baseline of Domain Randomisation (DR), or require substantial hyperparameter tuning to do so. Our analysis shows that this is due to their underlying scoring functions failing to predict intuitive measures of ``learnability'', i.e., in finding the settings that the agent sometimes solves, but not always. Based on this, we instead directly train on levels with high learnability and find that this simple and intuitive approach outperforms UED methods and DR in several binary-outcome environments, including on our domain and the standard UED domain of Minigrid. We further introduce a new adversarial evaluation procedure for directly measuring robustness, closely mirroring the conditional value at risk (CVaR). We open-source all our code and present visualisations of final policies here: https://github.com/amacrutherford/sampling-for-learnability.

Mixture of Experts in a Mixture of RL settings

Mixtures of Experts (MoEs) have gained prominence in (self-)supervised learning due to their enhanced inference efficiency, adaptability to distributed training, and modularity. Previous research has illustrated that MoEs can significantly boost Deep Reinforcement Learning (DRL) performance by expanding the network's parameter count while reducing dormant neurons, thereby enhancing the model's learning capacity and ability to deal with non-stationarity. In this work, we shed more light on MoEs' ability to deal with non-stationarity and investigate MoEs in DRL settings with "amplified" non-stationarity via multi-task training, providing further evidence that MoEs improve learning capacity. In contrast to previous work, our multi-task results allow us to better understand the underlying causes for the beneficial effect of MoE in DRL training, the impact of the various MoE components, and insights into how best to incorporate them in actor-critic-based DRL networks. Finally, we also confirm results from previous work.

Mixtures of Experts Unlock Parameter Scaling for Deep RL

The recent rapid progress in (self) supervised learning models is in large part predicted by empirical scaling laws: a model's performance scales proportionally to its size. Analogous scaling laws remain elusive for reinforcement learning domains, however, where increasing the parameter count of a model often hurts its final performance. In this paper, we demonstrate that incorporating Mixture-of-Expert (MoE) modules, and in particular Soft MoEs (Puigcerver et al., 2023), into value-based networks results in more parameter-scalable models, evidenced by substantial performance increases across a variety of training regimes and model sizes. This work thus provides strong empirical evidence towards developing scaling laws for reinforcement learning.

Analysing the Sample Complexity of Opponent Shaping

Learning in general-sum games often yields collectively sub-optimal results. Addressing this, opponent shaping (OS) methods actively guide the learning processes of other agents, empirically leading to improved individual and group performances in many settings. Early OS methods use higher-order derivatives to shape the learning of co-players, making them unsuitable for shaping multiple learning steps. Follow-up work, Model-free Opponent Shaping (M-FOS), addresses these by reframing the OS problem as a meta-game. In contrast to early OS methods, there is little theoretical understanding of the M-FOS framework. Providing theoretical guarantees for M-FOS is hard because A) there is little literature on theoretical sample complexity bounds for meta-reinforcement learning B) M-FOS operates in continuous state and action spaces, so theoretical analysis is challenging. In this work, we present R-FOS, a tabular version of M-FOS that is more suitable for theoretical analysis. R-FOS discretises the continuous meta-game MDP into a tabular MDP. Within this discretised MDP, we adapt the $R_{max}$ algorithm, most prominently used to derive PAC-bounds for MDPs, as the meta-learner in the R-FOS algorithm. We derive a sample complexity bound that is exponential in the cardinality of the inner state and action space and the number of agents. Our bound guarantees that, with high probability, the final policy learned by an R-FOS agent is close to the optimal policy, apart from a constant factor. Finally, we investigate how R-FOS's sample complexity scales in the size of state-action space. Our theoretical results on scaling are supported empirically in the Matching Pennies environment.

Leading the Pack: N-player Opponent Shaping

Reinforcement learning solutions have great success in the 2-player general sum setting. In this setting, the paradigm of Opponent Shaping (OS), in which agents account for the learning of their co-players, has led to agents which are able to avoid collectively bad outcomes, whilst also maximizing their reward. These methods have currently been limited to 2-player game. However, the real world involves interactions with many more agents, with interactions on both local and global scales. In this paper, we extend Opponent Shaping (OS) methods to environments involving multiple co-players and multiple shaping agents. We evaluate on over 4 different environments, varying the number of players from 3 to 5, and demonstrate that model-based OS methods converge to equilibrium with better global welfare than naive learning. However, we find that when playing with a large number of co-players, OS methods' relative performance reduces, suggesting that in the limit OS methods may not perform well. Finally, we explore scenarios where more than one OS method is present, noticing that within games requiring a majority of cooperating agents, OS methods converge to outcomes with poor global welfare.

Scaling Opponent Shaping to High Dimensional Games

In multi-agent settings with mixed incentives, methods developed for zero-sum games have been shown to lead to detrimental outcomes. To address this issue, opponent shaping (OS) methods explicitly learn to influence the learning dynamics of co-players and empirically lead to improved individual and collective outcomes. However, OS methods have only been evaluated in low-dimensional environments due to the challenges associated with estimating higher-order derivatives or scaling model-free meta-learning. Alternative methods that scale to more complex settings either converge to undesirable solutions or rely on unrealistic assumptions about the environment or co-players. In this paper, we successfully scale an OS-based approach to general-sum games with temporally-extended actions and long-time horizons for the first time. After analysing the representations of the meta-state and history used by previous algorithms, we propose a simplified version called Shaper. We show empirically that Shaper leads to improved individual and collective outcomes in a range of challenging settings from literature. We further formalize a technique previously implicit in the literature, and analyse its contribution to opponent shaping. We show empirically that this technique is helpful for the functioning of prior methods in certain environments. Lastly, we show that previous environments, such as the CoinGame, are inadequate for analysing temporally-extended general-sum interactions.

JaxMARL: Multi-Agent RL Environments in JAX

Benchmarks play an important role in the development of machine learning algorithms. For example, research in reinforcement learning (RL) has been heavily influenced by available environments and benchmarks. However, RL environments are traditionally run on the CPU, limiting their scalability with typical academic compute. Recent advancements in JAX have enabled the wider use of hardware acceleration to overcome these computational hurdles, enabling massively parallel RL training pipelines and environments. This is particularly useful for multi-agent reinforcement learning (MARL) research. First of all, multiple agents must be considered at each environment step, adding computational burden, and secondly, the sample complexity is increased due to non-stationarity, decentralised partial observability, or other MARL challenges. In this paper, we present JaxMARL, the first open-source code base that combines ease-of-use with GPU enabled efficiency, and supports a large number of commonly used MARL environments as well as popular baseline algorithms. When considering wall clock time, our experiments show that per-run our JAX-based training pipeline is up to 12500x faster than existing approaches. This enables efficient and thorough evaluations, with the potential to alleviate the evaluation crisis of the field. We also introduce and benchmark SMAX, a vectorised, simplified version of the popular StarCraft Multi-Agent Challenge, which removes the need to run the StarCraft II game engine. This not only enables GPU acceleration, but also provides a more flexible MARL environment, unlocking the potential for self-play, meta-learning, and other future applications in MARL. We provide code at https://github.com/flairox/jaxmarl.

Adversarial Cheap Talk

Adversarial attacks in reinforcement learning (RL) often assume highly-privileged access to the victim's parameters, environment, or data. Instead, this paper proposes a novel adversarial setting called a Cheap Talk MDP in which an Adversary can merely append deterministic messages to the Victim's observation, resulting in a minimal range of influence. The Adversary cannot occlude ground truth, influence underlying environment dynamics or reward signals, introduce non-stationarity, add stochasticity, see the Victim's actions, or access their parameters. Additionally, we present a simple meta-learning algorithm called Adversarial Cheap Talk (ACT) to train Adversaries in this setting. We demonstrate that an Adversary trained with ACT can still significantly influence the Victim's training and testing performance, despite the highly constrained setting. Affecting train-time performance reveals a new attack vector and provides insight into the success and failure modes of existing RL algorithms. More specifically, we show that an ACT Adversary is capable of harming performance by interfering with the learner's function approximation, or instead helping the Victim's performance by outputting useful features. Finally, we show that an ACT Adversary can manipulate messages during train-time to directly and arbitrarily control the Victim at test-time.

Model-Free Opponent Shaping

In general-sum games, the interaction of self-interested learning agents commonly leads to collectively worst-case outcomes, such as defect-defect in the iterated prisoner's dilemma (IPD). To overcome this, some methods, such as Learning with Opponent-Learning Awareness (LOLA), shape their opponents' learning process. However, these methods are myopic since only a small number of steps can be anticipated, are asymmetric since they treat other agents as naive learners, and require the use of higher-order derivatives, which are calculated through white-box access to an opponent's differentiable learning algorithm. To address these issues, we propose Model-Free Opponent Shaping (M-FOS). M-FOS learns in a meta-game in which each meta-step is an episode of the underlying ("inner") game. The meta-state consists of the inner policies, and the meta-policy produces a new inner policy to be used in the next episode. M-FOS then uses generic model-free optimisation methods to learn meta-policies that accomplish long-horizon opponent shaping. Empirically, M-FOS near-optimally exploits naive learners and other, more sophisticated algorithms from the literature. For example, to the best of our knowledge, it is the first method to learn the well-known Zero-Determinant (ZD) extortion strategy in the IPD. In the same settings, M-FOS leads to socially optimal outcomes under meta-self-play. Finally, we show that M-FOS can be scaled to high-dimensional settings.

COLA: Consistent Learning with Opponent-Learning Awareness

Learning in general-sum games can be unstable and often leads to socially undesirable, Pareto-dominated outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced opponent shaping to this setting, by accounting for the agent's influence on the anticipated learning steps of other agents. However, the original LOLA formulation (and follow-up work) is inconsistent because LOLA models other agents as naive learners rather than LOLA agents. In previous work, this inconsistency was suggested as a cause of LOLA's failure to preserve stable fixed points (SFPs). First, we formalize consistency and show that higher-order LOLA (HOLA) solves LOLA's inconsistency problem if it converges. Second, we correct a claim made in the literature, by proving that, contrary to Sch\"afer and Anandkumar (2019), Competitive Gradient Descent (CGD) does not recover HOLA as a series expansion. Hence, CGD also does not solve the consistency problem. Third, we propose a new method called Consistent LOLA (COLA), which learns update functions that are consistent under mutual opponent shaping. It requires no more than second-order derivatives and learns consistent update functions even when HOLA fails to converge. However, we also prove that even consistent update functions do not preserve SFPs, contradicting the hypothesis that this shortcoming is caused by LOLA's inconsistency. Finally, in an empirical evaluation on a set of general-sum games, we find that COLA finds prosocial solutions and that it converges under a wider range of learning rates than HOLA and LOLA. We support the latter finding with a theoretical result for a simple game.