Papers › Beyond Task Diversity: Provable Representation Transfer for Sequential Multi-Task...

Beyond Task Diversity: Provable Representation Transfer for Sequential Multi-Task Linear Bandits

23 Jan 2025arXiv:2501.13390archive 2025-07-28

Thang Duong, Zhi Wang, Chicheng Zhang

We study lifelong learning in linear bandits, where a learner interacts with a sequence of linear bandit tasks whose parameters lie in an m-dimensional subspace of ℝᵈ, thereby sharing a low-rank representation. Current literature typically assumes that the tasks are diverse, i.e., their parameters uniformly span the m-dimensional subspace. This assumption allows the low-rank representation to be learned before all tasks are revealed, which can be unrealistic in real-world applications. In this work, we present the first nontrivial result for sequential multi-task linear bandits without the task diversity assumption. We develop an algorithm that efficiently learns and transfers low-rank representations. When facing N tasks, each played over τ rounds, our algorithm achieves a regret guarantee of Õ(Nm √(τ) + N^(2/3) τ^(2/3) d m^(1/3) + Nd² + τm d ) under the ellipsoid action set assumption. This result can significantly improve upon the baseline of Õ (Nd √(τ)) that does not leverage the low-rank structure when the number of tasks N is sufficiently large and m ≪d. We also demonstrate empirically on synthetic data that our algorithm outperforms baseline algorithms, which rely on the task diversity assumption.

Code

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

13 samples harvested; 11 ran; 0 honoured the contract we drafted; 2 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.

Licence: 0 of the 13 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.

Harvested from duongnhatthang/BOSS. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.

Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.

Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.

Tasks

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections