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. K E Y W O R D Scalibration, drug treatment, genetic algorithm, high performance computing, model exploration Charilaos Akasiadis and Miguel Ponce-de-Leon contributed equally to this study. Arnau Montagud, Evangelos Michelioudakis, Alexia Atsidakou, and Elias Alevizos contributed equally to this study. Alexander Artikis, Alfonso Valencia, and Georgios Paliouras contributed equally to this study.

We study the statistical and computational complexities of the Polyak step size gradient descent algorithm under generalized smoothness and Lojasiewicz conditions of the population loss function, namely, the limit of the empirical loss function when the sample size goes to infinity, and the stability between the gradients of the empirical and population loss functions, namely, the polynomial growth on the concentration bound between the gradients of sample and population loss functions. We demonstrate that the Polyak step size gradient descent iterates reach a final statistical radius of convergence around the true parameter after logarithmic number of iterations in terms of the sample size. It is computationally cheaper than the polynomial number of iterations on the sample size of the fixed-step size gradient descent algorithm to reach the same final statistical radius when the population loss function is not locally strongly convex. Finally, we illustrate our general theory under three statistical examples: generalized linear model, mixture model, and mixed linear regression model.

Pandora's Box is a fundamental stochastic optimization problem, where the decisionmaker 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 priors are given for the values of all the alternatives, while recent work studies the online variant of Pandora's Box where priors are originally unknown. In this work, we extend Pandora's Box to 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 prior distribution that may change at every round. Our main result is a noregret 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 novel a modification of the realizability condition in contextual bandits that connects a context to the reservation value of the corresponding distribution rather than its mean.

Fixed-budget best-arm identification (BAI) is a bandit problem where the learning agent maximizes the probability of identifying the optimal arm after a fixed number of observations. In this work, we initiate the study of this problem in the Bayesian setting. We propose a Bayesian elimination algorithm and derive an upper bound on the probability that it fails to identify the optimal arm. The bound reflects the quality of the prior and is the first such bound in this setting. We prove it using a frequentist-like argument, where we carry the prior through, and then integrate out the random bandit instance at the end. Our upper bound asymptotically matches a newly established lower bound for 2 arms. Our experimental results show that Bayesian elimination is superior to frequentist methods and competitive with the state-of-the-art Bayesian algorithms that have no guarantees in our setting.