Finite-Time Logarithmic Bayes Regret Upper Bounds

We derive the first finite-time logarithmic Bayes regret upper bounds for Bayesian bandits. In a multi-armed bandit, we obtain $O(c_\Delta \log n)$ and $O(c_h \log^2 n)$ upper bounds for an upper confidence bound algorithm, where $c_h$ and $c_\Delta$ are constants depending on the prior distribution and the gaps of bandit instances sampled from it, respectively. The latter bound asymptotically matches the lower bound of Lai (1987). Our proofs are a major technical departure from prior works, while being simple and general. To show the generality of our techniques, we apply them to linear bandits. Our results provide insights on the value of prior in the Bayesian setting, both in the objective and as a side information given to the learner. They significantly improve upon existing $\tilde{O}(\sqrt{n})$ bounds, which have become standard in the literature despite the logarithmic lower bound of Lai (1987)

Contextual Pandora's Box

Pandora's Box is a fundamental stochastic optimization problem, where the decision-maker must find a good alternative while minimizing the search cost of exploring the value of each alternative. In the original formulation, it is assumed that accurate distributions are given for the values of all the alternatives, while recent work studies the online variant of Pandora's Box where the distributions are originally unknown. In this work, we study Pandora's Box in the online setting, while incorporating context. At every round, we are presented with a number of alternatives each having a context, an exploration cost and an unknown value drawn from an unknown distribution that may change at every round. Our main result is a no-regret algorithm that performs comparably well to the optimal algorithm which knows all prior distributions exactly. Our algorithm works even in the bandit setting where the algorithm never learns the values of the alternatives that were not explored. The key technique that enables our result is a novel modification of the realizability condition in contextual bandits that connects a context to a sufficient statistic of each alternative's distribution (its "reservation value") rather than its mean

Parallel model exploration for tumor treatment simulations

Abstract Computational systems and methods are often being used in biological research, including the understanding of cancer and the development of treatments. Simulations of tumor growth and its response to different drugs are of particular importance, but also challenging complexity. The main challenges are first to calibrate the simulators so as to reproduce real-world cases, and second, to search for specific values of the parameter space concerning effective drug treatments. In this work, we combine a multi-scale simulator for tumor cell growth and a genetic algorithm (GA) as a heuristic search method for finding good parameter configurations in reasonable time. The two modules are integrated into a single workflow that can be executed in parallel on high performance computing infrastructures. In effect, the GA is used to calibrate the simulator, and then to explore different drug delivery schemes. Among these schemes, we aim to find those that minimize tumor cell size and the probability of emergence of drug resistant cells in the future. Experimental results illustrate the effectiveness and computational efficiency of the approach.This work has received funding from the EU Horizon 2020 RIA program INFORE under grant agreement No 825070Peer ReviewedPostprint (author's final draft