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Begriffe
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Value Distribution

Complete representation of uncertainty about future returns in reinforcement learning, modeling the entire probability distribution of each possible return rather than just its expectation.

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Distributional Reinforcement Learning

RL paradigm that explicitly models the full distribution of expected returns to capture uncertainty and variability of future outcomes.

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Distributional Q-Function

Extension of the Q-value function that returns a probability distribution over expected returns instead of a single scalar value.

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Atomization Parametrization

Technique for discretizing continuous distributions into finite sets of points (atoms) with associated probabilities to facilitate computational learning.

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Categorical Distributional RL (C51)

Pioneering algorithm that models the return distribution as a discrete categorical distribution over a fixed support of values.

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Distributional Bellman Operator

Generalization of the classical Bellman operator that applies to full distributions rather than just expected values.

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Wasserstein Distance

Metric used to measure similarity between value distributions in the return space, allowing capture of both the location and shape of distributions.

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Distributional Projection

Process of projecting continuous distributions onto a predefined discrete support, essential for practical implementation of distributional algorithms.

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Distributional Risk

Measure of the uncertainty and variability in return predictions, quantified through the higher statistical moments of the value distribution.

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Higher-Order Moments

Statistics (variance, skewness, kurtosis) describing the shape of the return distribution beyond the mean, capturing asymmetry and probability concentration.

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Distributional Temporal Variation

Temporal evolution of the full shape of the return distribution rather than just its expected value, revealing changing risk patterns.

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Discrete Value Support

Finite and ordered set of values on which continuous distributions are approximated in practical distributional algorithms.

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Distributional Propagation

Process of updating value distributions via the Bellman operator, preserving uncertainty information at each time step.

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Distributional Stability

Property of convergence of value distributions to a stable form during learning, ensuring the consistency of uncertainty estimates.

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