A Distributional Framework for Risk-Sensitive End-to-End Planning in Continuous MDPs
Bibliographic record
Abstract
Recent advances in efficient planning in deterministic or stochastic high-dimensional domains with continuous action spaces leverage backpropagation through a model of the environment to directly optimize action sequences. However, existing methods typically do not take risk into account when optimizing in stochastic domains, which can be incorporated efficiently in MDPs by optimizing a nonlinear utility function of the return distribution. We bridge this gap by introducing Risk-Aware Planning using PyTorch (RAPTOR), a novel unified framework for risk-sensitive planning through end-to-end optimization of commonly-studied risk-sensitive utility functions such as entropic utility, mean-variance optimization and CVaR. A key technical difficulty of our approach is that direct optimization of general risk-sensitive utility functions by backpropagation is impossible due to the presence of environment stochasticity. The novelty of RAPTOR lies in leveraging reparameterization of the state distribution, leading to a unique distributional perspective of end-to-end planning where the return distribution is utilized for sampling as well as optimizing risk-aware objectives by backpropagation in a unified framework. We evaluate and compare RAPTOR on three highly stochastic MDPs, including nonlinear navigation, HVAC control, and linear reservoir control, demonstrating the ability of RAPTOR to manage risk in complex continuous domains according to different notions of risk-sensitive utility.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".