Policy Information Capacity: Information-Theoretic Measure for Task Complexity in Deep Reinforcement Learning (2103.12726v2)

Abstract: Progress in deep reinforcement learning (RL) research is largely enabled by benchmark task environments. However, analyzing the nature of those environments is often overlooked. In particular, we still do not have agreeable ways to measure the difficulty or solvability of a task, given that each has fundamentally different actions, observations, dynamics, rewards, and can be tackled with diverse RL algorithms. In this work, we propose policy information capacity (PIC) -- the mutual information between policy parameters and episodic return -- and policy-optimal information capacity (POIC) -- between policy parameters and episodic optimality -- as two environment-agnostic, algorithm-agnostic quantitative metrics for task difficulty. Evaluating our metrics across toy environments as well as continuous control benchmark tasks from OpenAI Gym and DeepMind Control Suite, we empirically demonstrate that these information-theoretic metrics have higher correlations with normalized task solvability scores than a variety of alternatives. Lastly, we show that these metrics can also be used for fast and compute-efficient optimizations of key design parameters such as reward shaping, policy architectures, and MDP properties for better solvability by RL algorithms without ever running full RL experiments.

• The paper presents PIC and POIC as novel metrics that use mutual information to quantify task complexity across various deep RL environments.
• It establishes a universal framework that outperforms conventional measures by correlating POIC with task solvability in both simple and complex settings.
• Empirical evaluations demonstrate that these metrics can guide optimization of experimental parameters and enhance reward shaping and neural architecture design.

Policy Information Capacity: An Information-Theoretic Measure for Task Complexity in Deep Reinforcement Learning

The paper introduces a novel metric titled "Policy Information Capacity" (PIC), alongside its variant, "Policy-Optimal Information Capacity" (POIC), which are proposed to quantitatively assess the complexity of tasks in deep reinforcement learning (RL) from an information-theoretic standpoint. These metrics address a significant gap in RL research, where the emphasis has predominantly been on algorithm development while the analysis of environment complexity has been scarce.

Methodological Contributions

1. Definition of PIC and POIC: The authors define PIC as the mutual information between policy parameters and the episodic return received from an environment. On the other hand, POIC measures the mutual information between policy parameters and episodic optimality, drawing from the control as inference literature. These metrics are non-specific to any particular RL algorithm or environment, offering a versatile approach to evaluating task difficulty.
2. Pareto Comparison with Existing Metrics: Unlike many conventional measures of task complexity, which are often tailored to specific algorithmic or environmental contexts (e.g., sample complexity in tabular MDPs), PIC and POIC provide a more universal framework. Specifically, POIC showed higher correlation with task solvability scores in benchmark environments compared to other alternatives, such as reward or return variances, traditionally used for similar purposes.
3. Empirical Evaluation: Empirical validations were performed across a range of environments—from simplified toy problems to complex and high-dimensional environments typical in RL benchmarks, such as those from OpenAI Gym and DeepMind Control Suite. The results suggest that POIC, in particular, is robust as an indicator of task solvability.
4. Implementation and Practical Utility: The practical utility of these metrics extends beyond mere assessment. PIC and POIC can guide the efficient optimization of various experimental parameters prior to the full deployment of RL algorithms. For example, these metrics can inform and optimize the reward shaping strategies, neural network architectures, and initialization parameters.

Theoretical Insights

The paper provides a theoretical rationale underpinning the metrics: maximizing PIC aligns with a dual objective of maximizing the diversity of achievable rewards while minimizing the unpredictability of rewards given specific policy parameters. This can be viewed as enhancing the controllability of the environment—critical for efficient task resolution by RL agents.

Future Directions

Key limitations acknowledge the dependency of the proposed metrics on the distribution of policy parameters $p(\theta)$. The local nature of these metrics suggests that their efficacy might vary considerably over different regions of the parameter space and across different phases of learning (exploration vs. exploitation). Future research should explore methods to adaptively refine these metrics throughout training, thereby aligning them more closely with the nuanced dynamics of policy learning. Additionally, expanding empirical assessments into domains that necessitate larger neural architectures and unbounded observational spaces, like visual input RL tasks, poses a compelling avenue for further paper.

Overall, the paper contributes significant advancements in RL by framing task complexity analysis in an information-theoretic context, shedding light on hereto overlooked dimensions of RL environment evaluations.