{"title": "Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards", "book": "Advances in Neural Information Processing Systems", "page_first": 11272, "page_last": 11281, "abstract": "Classical multi-armed bandit problems use the expected value of an arm as a metric\nto evaluate its goodness. However, the expected value is a risk-neutral metric. In\nmany applications like finance, one is interested in balancing the expected return\nof an arm (or portfolio) with the risk associated with that return. In this paper,\nwe consider the problem of selecting the arm that optimizes a linear combination\nof the expected reward and the associated Conditional Value at Risk (CVaR) in a\nfixed budget best-arm identification framework. We allow the reward distributions\nto be unbounded or even heavy-tailed. For this problem, our goal is to devise\nalgorithms that are entirely distribution oblivious, i.e., the algorithm is not aware of\nany information on the reward distributions, including bounds on the moments/tails,\nor the suboptimality gaps across arms.\nIn this paper, we provide a class of such algorithms with provable upper bounds\non the probability of incorrect identification. In the process, we develop a novel\nestimator for the CVaR of unbounded (including heavy-tailed) random variables\nand prove a concentration inequality for the same, which could be of independent\ninterest. We also compare the error bounds for our distribution oblivious algorithms\nwith those corresponding to standard non-oblivious algorithms. Finally, numerical\nexperiments reveal that our algorithms perform competitively when compared with\nnon-oblivious algorithms, suggesting that distribution obliviousness can be realised\nin practice without incurring a significant loss of performance.", "full_text": "\f\f\f\f\f\f\f\f\f\f", "award": [], "sourceid": 6022, "authors": [{"given_name": "Anmol", "family_name": "Kagrecha", "institution": "Indian Institute of Technology Bombay"}, {"given_name": "Jayakrishnan", "family_name": "Nair", "institution": "\"Assist. Prof, EE, IIT Bombay\""}, {"given_name": "Krishna", "family_name": "Jagannathan", "institution": "IIT Madras"}]}