In many practical reinforcement learning scenarios, feedback is provided only at the end of a long horizon, leading to sparse and delayed rewards. Existing reward redistribution methods typically assume that per-step rewards are independent, thus overlooking interdependencies among state--action pairs. In this paper, we propose a \emph{Likelihood Reward Redistribution} (LRR) framework that addresses this issue by modeling each per-step reward with a parametric probability distribution whose parameters depend on the state--action pair. By maximizing the likelihood of the observed episodic return via a leave-one-out (LOO) strategy that leverages the entire trajectory, our framework inherently introduces an uncertainty regularization term into the surrogate objective. Moreover, we show that the conventional mean squared error (MSE) loss for reward redistribution emerges as a special case of our likelihood framework when the uncertainty is fixed under the Gaussian distribution. When integrated with an off-policy algorithm such as Soft Actor-Critic, LRR yields dense and informative reward signals, resulting in superior sample efficiency and policy performance on Box-2d and MuJoCo benchmarks.

Risk-sensitive reinforcement learning (RL) is crucial for maintaining reliable performance in many high-stakes applications. While most RL methods aim to learn a point estimate of the random cumulative cost, distributional RL (DRL) seeks to estimate the entire distribution of it. The distribution provides all necessary information about the cost and leads to a unified framework for handling various risk measures in a risk-sensitive setting. However, developing policy gradient methods for risk-sensitive DRL is inherently more complex as it pertains to finding the gradient of a probability measure. This paper introduces a policy gradient method for risk-sensitive DRL with general coherent risk measures, where we provide an analytical form of the probability measure's gradient. We further prove the local convergence of the proposed algorithm under mild smoothness assumptions. For practical use, we also design a categorical distributional policy gradient algorithm (CDPG) based on categorical distributional policy evaluation and trajectory-based gradient estimation. Through experiments on a stochastic cliff-walking environment, we illustrate the benefits of considering a risk-sensitive setting in DRL.