Dichotomy of Control: Separating What You Can Control from What You Cannot (2210.13435v1)

Abstract: Future- or return-conditioned supervised learning is an emerging paradigm for offline reinforcement learning (RL), where the future outcome (i.e., return) associated with an observed action sequence is used as input to a policy trained to imitate those same actions. While return-conditioning is at the heart of popular algorithms such as decision transformer (DT), these methods tend to perform poorly in highly stochastic environments, where an occasional high return can arise from randomness in the environment rather than the actions themselves. Such situations can lead to a learned policy that is inconsistent with its conditioning inputs; i.e., using the policy to act in the environment, when conditioning on a specific desired return, leads to a distribution of real returns that is wildly different than desired. In this work, we propose the dichotomy of control (DoC), a future-conditioned supervised learning framework that separates mechanisms within a policy's control (actions) from those beyond a policy's control (environment stochasticity). We achieve this separation by conditioning the policy on a latent variable representation of the future, and designing a mutual information constraint that removes any information from the latent variable associated with randomness in the environment. Theoretically, we show that DoC yields policies that are consistent with their conditioning inputs, ensuring that conditioning a learned policy on a desired high-return future outcome will correctly induce high-return behavior. Empirically, we show that DoC is able to achieve significantly better performance than DT on environments that have highly stochastic rewards and transition

• The paper presents the DoC framework which uses mutual information constraints to differentiate controllable dynamics from environmental randomness in offline RL.
• It validates DoC with theory and experiments, showing superior performance over RCSL methods like the Decision Transformer in stochastic settings.
• The framework lays the groundwork for robust RL systems by offering actionable insights for managing randomness in sequential decision-making problems.

Dichotomy of Control: An Analysis

The paper "Dichotomy of Control: Separating What You Can Control from What You Cannot" introduces an innovative approach to tackling challenges in offline reinforcement learning (RL) by addressing the limitations of return-conditioned supervised learning (RCSL) in stochastic environments. The authors propose a novel methodology, termed the Dichotomy of Control (DoC), which distinguishes between policy-controllable dynamics and stochastic environmental factors. This work is anchored in the theoretical and empirical inadequacies of existing RCSL frameworks, including the Decision Transformer (DT), in contexts where randomness heavily influences outcomes.

Technical Contributions

The primary technical contribution of the paper is the development of the DoC framework, which employs a future-conditioned supervised learning paradigm. This framework incorporates a mutual information constraint to exclude environmental randomness from the latent variable representations that policies condition upon. Such a constraint ensures that the learned policies remain consistent with their conditioning inputs, thus rectifying the overoptimistic behaviors often induced by stochasticity in RCSL settings.

The paper provides a comprehensive theoretical foundation for DoC, demonstrating that it yields policies that reliably produce high-return behaviors when conditioned on high-return scenarios. The theoretical claims are substantiated through consistency guarantees, which are predicated on the mutual information constraints that disentangle controllable dynamics from stochastic transitions and rewards.

Empirical Validation

Empirically, the authors validate DoC across multiple experimental environments characterized by stochastic dynamics, namely a Bernoulli bandit problem, the FrozenLake setting, and modified Gym MuJoCo environments. These experiments collectively illustrate that DoC consistently outperforms both the Decision Transformer and a future-conditioned VAE approach, especially in highly stochastic scenarios with suboptimal offline data.

In the Bernoulli bandit setup, DoC approximates Bayes-optimal behavior, significantly surpassing RCSL by effectively identifying and exploiting the more rewarding actions in the face of environmental randomness. Similarly, in the FrozenLake and Gym MuJoCo environments, DoC demonstrated robustness and superior performance across a spectrum of stochastic conditions and dataset qualities.

Implications and Future Work

The implications of this research extend into both theoretical advancements and practical enhancements in offline reinforcement learning. Theoretical insights provided by DoC offer a deeper understanding of policy-learning mechanisms under stochastic influences and pave the way for designing more robust RL systems that can generalize across varying environmental conditions.

Practically, the DoC framework suggests a promising direction for leveraging large-scale supervised learning techniques in sequential decision-making tasks, especially where conventional RL fails due to stochastic disruptions or suboptimal data. The disentanglement principle advanced by DoC could potentially be adapted to other facets of AI, where distinguishing controllable and uncontrollable factors is pivotal.

Future research directions may focus on expanding the DoC methodology to cater to more complex environments and reward structures, exploring hierarchical policy-learning coupled with disentanglement, or integrating DoC with other RL paradigms, such as model-based approaches, to capitalize on their respective strengths.

In conclusion, the Dichotomy of Control framework represents a significant step forward in addressing the inherent challenges of offline RL in stochastic environments, bridging a crucial gap between theoretical rigor and empirical validation in RL research.