On the Minimax Regret for Online Learning with Feedback Graphs
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
In this work, we improve on the upper and lower bounds for the regret of online learning with strongly observable undirected feedback graphs. The best known upper bound for this problem is $\mathcal{O}\bigl(\sqrt{αT\ln K}\bigr)$, where $K$ is the number of actions, $α$ is the independence number of the graph, and $T$ is the time horizon. The $\sqrt{\ln K}$ factor is known to be necessary when $α= 1$ (the experts case). On the other hand, when $α= K$ (the bandits case), the minimax rate is known to be $Θ\bigl(\sqrt{KT}\bigr)$, and a lower bound $Ω\bigl(\sqrt{αT}\bigr)$ is known to hold for any $α$. Our improved upper bound $\mathcal{O}\bigl(\sqrt{αT(1+\ln(K/α))}\bigr)$ holds for any $α$ and matches the lower bounds for bandits and experts, while interpolating intermediate cases. To prove this result, we use FTRL with $q$-Tsallis entropy for a carefully chosen value of $q \in [1/2, 1)$ that varies with $α$. The analysis of this algorithm requires a new bound on the variance term in the regret. We also show how to extend our techniques to time-varying graphs, without requiring prior knowledge of their independence numbers. Our upper bound is complemented by an improved $Ω\bigl(\sqrt{αT(\ln K)/(\lnα)}\bigr)$ lower bound for all $α> 1$, whose analysis relies on a novel reduction to multitask learning. This shows that a logarithmic factor is necessary as soon as $α< K$.
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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| 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