Convergence and Near Optimality of Q-Learning with Finite Memory for Partially Observed Models
Why this work is in the frame
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Bibliographic record
Abstract
Q learning algorithm is a popular reinforcement learning method for finite state/action fully observed Markov decision processes (MDPs). In this paper, we make two contributions: (i) we establish the convergence of a Q learning algorithm for partially observed Markov decision processes (POMDPs) using a finite history of past observations and control actions and show that the limit fixed point equation gives an optimal solution for an approximate belief-MDP. We then provide bounds on the performance of the policy obtained using the limit Q values compared to the performance of the optimal policy for the POMDP, where we also present explicit performance guarantees using recent results on filter stability in controlled POMDPs. (ii) We apply these results to fully observed MDPs with continuous state spaces and establish the near optimality of learned policies via quantization of the state space, where the quantization is viewed as a measurement channel leading to a POMDP model and a history of unit window size is considered. In particular, we show that Q-learning, with its convergence and near optimality properties, is applicable for continuous space MDPs when the state space is quantized.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it