{"paper":{"title":"Continuum armed bandit problem of few variables in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Bernd G\\\"artner, Hemant Tyagi","submitted_at":"2013-04-21T20:03:23Z","abstract_excerpt":"We consider the stochastic and adversarial settings of continuum armed bandits where the arms are indexed by [0,1]^d. The reward functions r:[0,1]^d -> R are assumed to intrinsically depend on at most k coordinate variables implying r(x_1,..,x_d) = g(x_{i_1},..,x_{i_k}) for distinct and unknown i_1,..,i_k from {1,..,d} and some locally Holder continuous g:[0,1]^k -> R with exponent 0 < alpha <= 1. Firstly, assuming (i_1,..,i_k) to be fixed across time, we propose a simple modification of the CAB1 algorithm where we construct the discrete set of sampling points to obtain a bound of O(n^((alpha+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5793","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}