{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/contextual-combinatorial-volatile-bandits-via","title":"Contextual Combinatorial Bandits with Changing Action Sets via Gaussian Processes","arxiv_id":"2110.02248","date":"2021-10-05","proceeding":null,"authors":["Andi Nika","Sepehr Elahi","Cem Tekin"],"abstract":"We consider a contextual bandit problem with a combinatorial action set and time-varying base arm availability. At the beginning of each round, the agent observes the set of available base arms and their contexts and then selects an action that is a feasible subset of the set of available base arms to maximize its cumulative reward in the long run. We assume that the mean outcomes of base arms are samples from a Gaussian Process (GP) indexed by the context set ${\\cal X}$, and the expected reward is Lipschitz continuous in expected base arm outcomes. For this setup, we propose an algorithm called Optimistic Combinatorial Learning and Optimization with Kernel Upper Confidence Bounds (O'CLOK-UCB) and prove that it incurs $\\tilde{O}(\\sqrt{\\lambda^*(K)KT\\overline{\\gamma}_{T}} )$ regret with high probability, where $\\overline{\\gamma}_{T}$ is the maximum information gain associated with the set of base arm contexts that appeared in the first $T$ rounds, $K$ is the maximum cardinality of any feasible action over all rounds and $\\lambda^*(K)$ is the maximum eigenvalue of all covariance matrices of selected actions up to time $T$, which is a function of $K$. To dramatically speed up the algorithm, we also propose a variant of O'CLOK-UCB that uses sparse GPs. Finally, we experimentally show that both algorithms exploit inter-base arm outcome correlation and vastly outperform the previous state-of-the-art UCB-based algorithms in realistic setups.","url_abs":"https://arxiv.org/abs/2110.02248v2","url_pdf":"https://arxiv.org/pdf/2110.02248v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"contextual-combinatorial-volatile-bandits-via","repo_url":"https://github.com/bilkent-cyborg/oclok-ucb","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"gaussian-process","method_name":"Gaussian Process"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=2110.02248","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2110.02248"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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