Learning with an objective to minimize the mismatch with a reference distribution has been shown to be useful for generative modeling and imitation learning. In this paper, we investigate whether one such objective, the Wasserstein-1 distance between a policy's state visitation distribution and a target distribution, can be utilized effectively for reinforcement learning (RL) tasks. Specifically, this paper focuses on goal-conditioned reinforcement learning where the idealized (unachievable) target distribution has full measure at the goal. This paper introduces a quasimetric specific to Markov Decision Processes (MDPs) and uses this quasimetric to estimate the above Wasserstein-1 distance. It further shows that the policy that minimizes this Wasserstein-1 distance is the policy that reaches the goal in as few steps as possible. Our approach, termed Adversarial Intrinsic Motivation (AIM), estimates this Wasserstein-1 distance through its dual objective and uses it to compute a supplemental reward function. Our experiments show that this reward function changes smoothly with respect to transitions in the MDP and directs the agent's exploration to find the goal efficiently. Additionally, we combine AIM with Hindsight Experience Replay (HER) and show that the resulting algorithm accelerates learning significantly on several simulated robotics tasks when compared to other rewards that encourage exploration or accelerate learning.

In thispaper,weinvestigatewhether onesuchobjective,theWasserstein-1 distance between a policy's state visitation distribution and a target distribution, can be utilized effectivelyforreinforcement learning (RL)tasks.

Behaviour cloning (BC) is a classic algorithm to imitate expert demonstrations [7], which uses supervised learning to greedily match the expert behaviour at demonstrated expert states. Due to environmentstochasticity,covariateshift,andpolicyapproximationerror,theagentmaydriftaway from the expert state distribution and ultimately fail to mimic the demonstrator [8].

In this paper, we propose a new off-policy estimator that applies IS directly on the stationary state-visitation distributions to avoid the exploding variance faced by existing methods.

The following lemma justifies item 3 in Assumption 1. Consider the following two cases: 1. Density function of the policy is smooth, i.e. We then show how Theorem 4 implies Theorem 1. Assumption 3. F or all x X, there exist constants such that the following hold 1. F or all x, we have null A Now we proceed to prove the main theorem. Then, given the above convergence result on the gradient norm, we proceed to prove the convergence of NAC in terms of the function value.

We draw an analogy between static friction in classical mechanics and extrapolation error in off-policy RL, and use it to formulate a constraint that prevents the policy from drifting toward unsupported actions. In this study, we present Frictional Q-learning, a deep reinforcement learning algorithm for continuous control, which extends batch-constrained reinforcement learning. Our algorithm constrains the agent's action space to encourage behavior similar to that in the replay buffer, while maintaining a distance from the manifold of the orthonormal action space. The constraint preserves the simplicity of batch-constrained, and provides an intuitive physical interpretation of extrapolation error. Empirically, we further demonstrate that our algorithm is robustly trained and achieves competitive performance across standard continuous control benchmarks.