Incremental Stochastic Factorization for Online Reinforcement Learning
Bibliographic record
Abstract
A construct that has been receiving attention recently in reinforcement learning is stochastic factorization (SF), a particular case of non-negative factorization (NMF) in which the matrices involved are stochastic. The idea is to use SF to approximate the transition matrices of a Markov decision process (MDP). This is useful for two reasons. First, learning the factors of the SF instead of the transition matrices can reduce significantly the number of parameters to be estimated. Second, it has been shown that SF can be used to reduce the number of operations needed to compute an MDP's value function. Recently, an algorithm called expectation-maximization SF (EMSF) has been proposed to compute a SF directly from transitions sampled from an MDP. In this paper we take a closer look at EMSF. First, by exploiting the assumptions underlying the algorithm, we show that it is possible to reduce it to simple multiplicative update rules similar to the ones that helped popularize NMF. Second, we analyze the optimization process underlying EMSF and find that it minimizes a modified version of the Kullback-Leibler divergence that is particularly well-suited for learning a SF from data sampled from an arbitrary distribution. Third, we build on this improved understanding of EMSF to draw an interesting connection with NMF and probabilistic latent semantic analysis. We also exploit the simplified update rules to introduce a new version of EMSF that generalizes and significantly improves its precursor. This new algorithm provides a practical mechanism to control the trade-off between memory usage and computing time, essentially freeing the space complexity of EMSF from its dependency on the number of sample transitions. The algorithm can also compute its approximation incrementally, which makes it possible to use it concomitantly with the collection of data. This feature makes the new version of EMSF particularly suitable for online reinforcement learning. Empirical results support the utility of the proposed algorithm.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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 source (direct Gemma or distilled Codex), 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".