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  1. Scott, Jacob G. (Ed.)
    The design of efficient combination therapies is a difficult key challenge in the treatment of complex diseases such as cancers. The large heterogeneity of cancers and the large number of available drugs renders exhaustive in vivo or even in vitro investigation of possible treatments impractical. In recent years, sophisticated mechanistic, ordinary differential equation-based pathways models that can predict treatment responses at a molecular level have been developed. However, surprisingly little effort has been put into leveraging these models to find novel therapies. In this paper we use for the first time, to our knowledge, a large-scale state-of-the-art pan-cancer signaling pathway model to identify candidates for novel combination therapies to treat individual cancer cell lines from various tissues (e.g., minimizing proliferation while keeping dosage low to avoid adverse side effects) and populations of heterogeneous cancer cell lines (e.g., minimizing the maximum or average proliferation across the cell lines while keeping dosage low). We also show how our method can be used to optimize the drug combinations used in sequential treatment plans—that is, optimized sequences of potentially different drug combinations—providing additional benefits. In order to solve the treatment optimization problems, we combine the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm with a significantly more scalable sampling scheme for truncated Gaussian distributions, based on a Hamiltonian Monte-Carlo method. These optimization techniques are independent of the signaling pathway model, and can thus be adapted to find treatment candidates for other complex diseases than cancers as well, as long as a suitable predictive model is available. 
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  2. null (Ed.)
    Tree-form sequential decision making (TFSDM) extends classical one-shot decision making by modeling tree-form interactions between an agent and a potentially adversarial environment. It captures the online decision-making problems that each player faces in an extensive-form game, as well as Markov decision processes and partially-observable Markov decision processes where the agent conditions on observed history. Over the past decade, there has been considerable effort into designing online optimization methods for TFSDM. Virtually all of that work has been in the full-feedback setting, where the agent has access to counterfactuals, that is, information on what would have happened had the agent chosen a different action at any decision node. Little is known about the bandit setting, where that assumption is reversed (no counterfactual information is available), despite this latter setting being well understood for almost 20 years in one-shot decision making. In this paper, we give the first algorithm for the bandit linear optimization problem for TFSDM that offers both (i) linear-time iterations (in the size of the decision tree) and (ii) O(T−−√) cumulative regret in expectation compared to any fixed strategy, at all times T. This is made possible by new results that we derive, which may have independent uses as well: 1) geometry of the dilated entropy regularizer, 2) autocorrelation matrix of the natural sampling scheme for sequence-form strategies, 3) construction of an unbiased estimator for linear losses for sequence-form strategies, and 4) a refined regret analysis for mirror descent when using the dilated entropy regularizer. 
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  3. We initiate the study of equilibrium refinements based on trembling-hand perfection in extensive-form games with commitment strategies, that is, where one player commits to a strategy first. We show that the standard strong (and weak) Stackelberg equilibria are not suitable for trembling-hand perfection, because the limit of a sequence of such strong (weak) Stackelberg commitment strategies of a perturbed game may not be a strong (weak) Stackelberg equilibrium itself. However, we show that the universal set of all Stackelberg equilibria (i.e., those that are optimal for at least some follower response function) is natural for trembling- hand perfection: it does not suffer from the problem above. We also prove that determining the existence of a Stackelberg equilibrium--refined or not--that gives the leader expected value at least v is NP-hard. This significantly extends prior complexity results that were specific to strong Stackelberg equilibrium. 
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