aiqbench analysis
This research proposes a Generalized Gaussian Distribution to better model the heavy-tailed residuals inherent in uncertainty-aware reinforcement learning, moving beyond standard zero-mean Gaussian assumptions. By introducing a state-conditioned shape head and Batch Inverse Error Variance regularization, the method offers improved performance across various control benchmarks where traditional approaches fall short. The study highlights that gains are task-dependent but validates a more robust statistical approach for handling nonstationary TD errors in complex environments.
Generalized Gaussian Temporal Difference Error for Uncertainty-aware Reinforcement Learning
arXiv:2408.02295v4 Announce Type: replace-cross Abstract: Conventional uncertainty-aware temporal difference (TD) learning often models TD errors as zero-mean Gaussian. This assumption can miss the heavy-tailed and heteroscedastic residuals induced by bootstrapping and exploration. We introduce a state-conditioned shape head based on the Generalized Gaussian Distribution (GGD) and use a numerically modified GGD loss as an online surrogate for nonstationary TD residuals. We distinguish two mathematical facts that are sometimes conflated: the exact GGD likelihood is normalized for every $\beta>0$, whereas its exponential density kernel is positive definite for $\beta\in(0,2]$. We use the learned shape to construct a simple monotone weighting heuristic and propose Batch Inverse Error Variance (BIEV) regularization from the variance and sample excess kurtosis of ensemble TD errors. Across continuous and discrete control benchmarks, the shape-aware variants improve over Gaussian-based variants in several settings, although the gains are task- and regime-dependent.
Abstract:Conventional uncertainty-aware temporal difference (TD) learning often models TD errors as zero-mean Gaussian. This assumption can miss the heavy-tailed and heteroscedastic residuals induced by bootstrapping and exploration. We introduce a state-conditioned shape head based on the Generalized Gaussian Distribution (GGD) and use a numerically modified GGD loss as an online surrogate for nonstationary TD residuals. We distinguish two mathematical facts that are sometimes conflated: the exact GGD likelihood is normalized for every $\beta>0$, whereas its exponential density kernel is positive definite for $\beta\in(0,2]$. We use the learned shape to construct a simple monotone weighting heuristic and propose Batch Inverse Error Variance (BIEV) regularization from the variance and sample excess kurtosis of ensemble TD errors. Across continuous and discrete control benchmarks, the shape-aware variants improve over Gaussian-based variants in several settings, although the gains are task- and regime-dependent.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Probability (math.PR); Machine Learning (stat.ML)
arXiv:2408.02295 [cs.LG]
(or arXiv:2408.02295v4 [cs.LG] for this version)
Full text under the publisher's open licence · 156 words
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