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Distributional Reinforcement Learning

Reinforcement learning paradigm that models the complete distribution of returns rather than just their mathematical expectation to capture uncertainty and improve robustness.

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Quantile Regression DQN

Distributional RL algorithm using quantile regression to approximate the return distribution as a set of quantiles, allowing fine-grained distribution estimation.

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Categorical DQN (C51)

Distributional RL method that discretizes the return distribution into 51 probability atoms, learning a categorical distribution to represent value uncertainty.

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Value Distribution

Complete probability distribution of expected future returns for a state-action pair, replacing the traditional single-value expectation approach.

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Risk-Sensitive RL

Reinforcement learning approach that explicitly considers risk by using the complete return distribution rather than just the mean for decision making.

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Wasserstein Distance

Metric used in Distributional RL to measure the distance between probability distributions, particularly effective for comparing distributions with different supports.

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Distributional Bellman Equation

Extension of the classical Bellman equation that operates on return distributions rather than scalar values, preserving the complete distribution information.

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Projected Bellman Operator

Operator that projects the updated return distribution onto the chosen parameterized representation space, ensuring stability of distributional learning.

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Aleatoric Uncertainty

Intrinsic and irreducible uncertainty in environment returns, naturally captured by Distributional RL models through the variance of the distribution.

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Epistemic Uncertainty

Uncertainty due to lack of knowledge or data, which can be reduced with more experience and modeled through the evolution of distributions during learning.

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Expectile Regression

Regression method that generalizes the notion of quantile for symmetric distributions, used in some Distributional RL algorithms to efficiently approximate distributions.

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Distributional Value Function

Function that associates each state-action pair with a complete probability distribution over future returns, replacing the traditional scalar value function.

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Categorical Projection

Mathematical operation used in C51 to project the updated return distribution onto the predefined discrete support of categorical atoms.

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Quantile Projection

Mechanism in QR-DQN that maintains a set of quantiles as an approximation of the distribution, directly updating the positions of quantiles without explicit projection.

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Distributional Policy Evaluation

Process of evaluating a policy by learning the complete distribution of returns rather than just their expected value, providing a richer analysis of performance.

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Implicit Quantile Networks (IQN)

Advanced network architecture that can generate any quantile of the return distribution on the fly, offering a continuous and flexible representation of distributions.

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Distributional Bellman Backup

Distributional RL update operation that propagates reward and transition distributions to compute the new value distribution according to the distributional Bellman equation.

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Return Distribution Modeling

Fundamental technique of Distributional RL that involves explicitly modeling the probability distribution of cumulative returns rather than just their mathematical expectation.

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