Distributions as Actions: A Unified Framework for Diverse Action Spaces
Bibliographic record
Abstract
We introduce a novel reinforcement learning (RL) framework that treats parameterized action distributions as actions, redefining the boundary between agent and environment. This reparameterization makes the new action space continuous, regardless of the original action type (discrete, continuous, hybrid, etc.). Under this new parameterization, we develop a generalized deterministic policy gradient estimator, Distributions-as-Actions Policy Gradient (DA-PG), which has lower variance than the gradient in the original action space. Although learning the critic over distribution parameters poses new challenges, we introduce Interpolated Critic Learning (ICL), a simple yet effective strategy to enhance learning, supported by insights from bandit settings. Building on TD3, a strong baseline for continuous control, we propose a practical actor-critic algorithm, Distributions-as-Actions Actor-Critic (DA-AC). Empirically, DA-AC achieves competitive performance in various settings across discrete, continuous, and hybrid control.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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".