[Paper Review] Invariant Causal Prediction for Block MDPs

Amy Zhang, Clare Lyle+6 more|arXiv (Cornell University)|Mar 12, 2020

Machine Learning and Algorithms31 references37 citations

TL;DR

The paper introduces invariant causal prediction (ICP) to learn model-irrelevance state abstractions (MISA) in Block MDPs, enabling generalization across environments and providing theoretical bounds, with linear and nonlinear experiments showing improved generalization over baselines.

ABSTRACT

Generalization across environments is critical to the successful application of reinforcement learning algorithms to real-world challenges. In this paper, we consider the problem of learning abstractions that generalize in block MDPs, families of environments with a shared latent state space and dynamics structure over that latent space, but varying observations. We leverage tools from causal inference to propose a method of invariant prediction to learn model-irrelevance state abstractions (MISA) that generalize to novel observations in the multi-environment setting. We prove that for certain classes of environments, this approach outputs with high probability a state abstraction corresponding to the causal feature set with respect to the return. We further provide more general bounds on model error and generalization error in the multi-environment setting, in the process showing a connection between causal variable selection and the state abstraction framework for MDPs. We give empirical evidence that our methods work in both linear and nonlinear settings, attaining improved generalization over single- and multi-task baselines.

Motivation & Objective

• Motivate robust generalization in reinforcement learning when observations vary across environments but latent dynamics are shared.
• Propose and formalize a block MDP framework with environment interventions to identify causal, task-relevant state features.
• Leverage invariant causal prediction to extract a model-irrelevance state abstraction suitable for generalization across environments.
• Provide theoretical bounds connecting causal variable selection to state abstractions and demonstrate practical performance in linear and nonlinear settings.

Proposed method

• Formulate Block MDPs with shared latent dynamics and environment-specific observations, introducing interventions on observation components.
• Apply invariant causal prediction (ICP) to identify causal ancestors of the reward and construct model-irrelevance state abstractions (MISA).
• Provide two learning approaches: a linear ICP-based variable selection method (Algorithm 1) and a nonlinear, gradient-based MISA objective (Algorithm 2) resembling invariant risk minimization (IRM).
• Derive generalization bounds linking model error to bisimulation with learned abstractions and present bounds on Q/value differences under invariant representations.
• Show that in linear settings, ICP can recover minimal causal feature sets; in nonlinear settings, optimize invariant representations across multiple environments.

Experimental results

Research questions

• RQ1 Can invariant causal prediction identify a minimal causal feature set that governs returns across Block MDP environments?
• RQ2 Do model-irrelevance state abstractions (MISA) learned via ICP generalize to unseen environments with shared latent dynamics?
• RQ3 What theoretical guarantees (error bounds) can connect causal variable selection to state abstraction quality in multi-environment RL?
• RQ4 Do linear and nonlinear MISA methods improve generalization against spurious correlations compared to baselines in practice?

Key findings

• Under Assumptions 1–3, a state abstraction based on causal ancestors of the reward provides a model-irrelevance abstraction for every environment in the family.
• In linear settings, ICP can recover the minimal causal feature set that generalizes across environments, eliminating spurious variables that harm generalization.
• The nonlinear MISA approach (gradient-based) yields improved generalization over single-task, multi-task baselines, and IRM in empirical tests on DeepMind Control tasks.
• Theoretical results connect learned abstractions to bisimulation and provide bounds on model error and Q/value differences when using invariant representations.
• Aggregate-sample generalization bounds scale with the total number of samples across all training environments rather than the number of environments.