Weak convergence properties of constrained emphatic temporal-difference learning with constant and slowly diminishing stepsize
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
We consider the emphatic temporal-difference (TD) algorithm, ETD(λ), for learning the value functions of stationary policies in a discounted, finite state and action Markov decision process. The ETD(λ) algorithm was recently proposed by Sutton, Mahmood, and White (2016) to solve a long-standing divergence problem of the standard TD algorithm when it is applied to off-policy training, where data from an exploratory policy are used to evaluate other policies of interest. The almost sure convergence of ETD(λ) has been proved in our recent work under general off-policy training conditions, but for a narrow range of diminishing stepsize. In this paper we present convergence results for constrained versions of ETD(λ) with constant stepsize and with diminishing stepsize from a broad range. Our results characterize the asymptotic behavior of the trajectory of iterates produced by those algorithms, and are derived by combining key properties of ETD(λ) with powerful convergence theorems from the weak convergence methods in stochastic approximation theory. For the case of constant stepsize, in addition to analyzing the behavior of the algorithms in the limit as the stepsize parameter approaches zero, we also analyze their behavior for a fixed stepsize and bound the deviations of their averaged iterates from the desired solution. These results are obtained by exploiting the weak Feller property of the Markov chains associated with the algorithms, and by using ergodic theorems for weak Feller Markov chains, in conjunction with the convergence results we get from the weak convergence methods. Besides ETD(λ), our analysis also applies to the off-policy TD(λ) algorithm, when the divergence issue is avoided by setting λ sufficiently large. It yields, for that case, new results on the asymptotic convergence properties of constrained off-policy TD(λ) with constant or slowly diminishing stepsize.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.005 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| 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 it