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Record W4392270931 · doi:10.48550/arxiv.2402.17235

Stochastic Gradient Succeeds for Bandits

2024· preprint· en· W4392270931 on OpenAlex

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.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenuearXiv (Cornell University) · 2024
Typepreprint
Languageen
FieldDecision Sciences
TopicAdvanced Bandit Algorithms Research
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaCanadian Institute for Advanced Research
KeywordsMathematical economicsComputer scienceEconomicsEconometricsMathematics

Abstract

fetched live from OpenAlex

We show that the \emph{stochastic gradient} bandit algorithm converges to a \emph{globally optimal} policy at an $O(1/t)$ rate, even with a \emph{constant} step size. Remarkably, global convergence of the stochastic gradient bandit algorithm has not been previously established, even though it is an old algorithm known to be applicable to bandits. The new result is achieved by establishing two novel technical findings: first, the noise of the stochastic updates in the gradient bandit algorithm satisfies a strong ``growth condition'' property, where the variance diminishes whenever progress becomes small, implying that additional noise control via diminishing step sizes is unnecessary; second, a form of ``weak exploration'' is automatically achieved through the stochastic gradient updates, since they prevent the action probabilities from decaying faster than $O(1/t)$, thus ensuring that every action is sampled infinitely often with probability $1$. These two findings can be used to show that the stochastic gradient update is already ``sufficient'' for bandits in the sense that exploration versus exploitation is automatically balanced in a manner that ensures almost sure convergence to a global optimum. These novel theoretical findings are further verified by experimental results.

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 imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: none
Teacher disagreement score0.899
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.002
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0020.003
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.001

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.

Opus teacher head0.291
GPT teacher head0.327
Teacher spread0.037 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it