Problem
Research questions and friction points this paper is trying to address.
inverse reinforcement learning
counterfactual gradient
adaptive IRL
Malliavin calculus
gradient estimation
Malliavin Calculus for Counterfactual Gradient Estimation in Adaptive Inverse Reinforcement Learning
🤖 AI Summary
This work addresses the challenge of estimating gradients under counterfactual (zero-probability) conditions in adaptive inverse reinforcement learning from passive observational data, where conventional Monte Carlo or kernel smoothing approaches suffer from low efficiency and slow convergence. The paper introduces Malliavin calculus to this domain for the first time, leveraging Skorohod integration to reformulate counterfactual gradients as ratios of unconditional expectations. Building upon this formulation, an efficient gradient estimator is developed by integrating Langevin dynamics. The proposed method accommodates general Langevin structures, recovers standard convergence rates, and significantly enhances both the accuracy and computational efficiency of loss function reconstruction.
📝 Abstract
Inverse reinforcement learning (IRL) recovers the loss function of a forward learner from its observed responses adaptive IRL aims to reconstruct the loss function of a forward learner by passively observing its gradients as it performs reinforcement learning (RL). This paper proposes a novel passive Langevin-based algorithm that achieves adaptive IRL. The key difficulty in adaptive IRL is that the required gradients in the passive algorithm are counterfactual, that is, they are conditioned on events of probability zero under the forward learner's trajectory. Therefore, naive Monte Carlo estimators are prohibitively inefficient, and kernel smoothing, though common, suffers from slow convergence. We overcome this by employing Malliavin calculus to efficiently estimate the required counterfactual gradients. We reformulate the counterfactual conditioning as a ratio of unconditioned expectations involving Malliavin quantities, thus recovering standard estimation rates. We derive the necessary Malliavin derivatives and their adjoint Skorohod integral formulations for a general Langevin structure, and provide a concrete algorithmic approach which exploits these for counterfactual gradient estimation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Malliavin calculus
counterfactual gradient estimation
adaptive inverse reinforcement learning
Langevin dynamics
Skorohod integral
🔎 Similar Papers
No similar papers found.
