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1. Acceptability maximization

   https://doi.org/10.3934/fmf.2021009  

   Kováčová, Gabriela; Rudloff, Birgit; Cialenco, Igor (January 2022, Frontiers of Mathematical Finance)

   The aim of this paper is to study the optimal investment problem by using coherent acceptability indices (CAIs) as a tool to measure the portfolio performance. We call this problem the acceptability maximization. First, we study the one-period (static) case, and propose a numerical algorithm that approximates the original problem by a sequence of risk minimization problems. The results are applied to several important CAIs, such as the gain-to-loss ratio, the risk-adjusted return on capital and the tail-value-at-risk based CAI. In the second part of the paper we investigate the acceptability maximization in a discrete time dynamic setup. Using robust representations of CAIs in terms of a family of dynamic coherent risk measures (DCRMs), we establish an intriguing dichotomy: if the corresponding family of DCRMs is recursive (i.e. strongly time consistent) and assuming some recursive structure of the market model, then the acceptability maximization problem reduces to just a one period problem and the maximal acceptability is constant across all states and times. On the other hand, if the family of DCRMs is not recursive, which is often the case, then the acceptability maximization problem ordinarily is a time-inconsistent stochastic control problem, similar to the classical mean-variance criteria. To overcome this form of time-inconsistency, we adapt to our setup the set-valued Bellman's principle recently proposed in [23] applied to two particular dynamic CAIs - the dynamic risk-adjusted return on capital and the dynamic gain-to-loss ratio. The obtained theoretical results are illustrated via numerical examples that include, in particular, the computation of the intermediate mean-risk efficient frontiers. 

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2. Adversarial influence maximization

   https://doi.org/10.1109/ISIT.2019.8849828  

   Khim, Justin; Jog, Varun; Loh, Po-Ling (January 2019, 2019 IEEE International Symposium on Information Theory (ISIT))
3. UTILITY MAXIMIZATION IN A LARGE MARKET: UTILITY MAXIMIZATION IN A LARGE MARKET

   https://doi.org/10.1111/mafi.12123  

   Mostovyi, Oleksii (May 2016, Mathematical Finance)
4. Decentralized Online Influence Maximization

   https://doi.org/10.1109/Allerton49937.2022.9929315  

   Bayiz, Yigit E.; Topcu, Ufuk (September 2022, 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton))

   We consider the problem of finding the maximally influential node in random networks where each node influences every other node with constant yet unknown probability. We develop an online algorithm that learns the relative influences of the nodes. It relaxes the assumption in the existing literature that a central observer can monitor the influence spread globally. The proposed algorithm delegates the online updates to the nodes on the network; hence requires only local observations at the nodes. We show that using an explore-then-commit learning strategy, the cumulative regret accumulated by the algorithm over horizon T approaches O(T2/3) for a network with a large number of nodes. Additionally, we show that, for fixed T, the worst case-regret grows linearly with the number n of nodes in the graph. Numerical experiments illustrate this linear dependence for Chung-Lu models. The experiments also demonstrate that ε-greedy learning strategies can achieve similar performance to the explore-then-commit strategy on Chung-Lu models. 

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5. Distributionally Robust Submodular Maximization

   Staib, M.; Wilder, B.; Jegelka, S. (April 2019, Proceedings of the International Workshop on Artificial Intelligence and Statistics)

   ubmodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function f . We focus on stochastic functions that are given as an expectation of functions over a distribution P. In practice, we often have only a limited set of samples fi from P . The standard approach indirectly optimizes f by maximizing the sum of fi. However, this ignores generalization to the true (unknown) distribution. In this paper, we achieve better performance on the actual underlying function f by directly optimizing a combination of bias and variance. Algorith- mically, we accomplish this by showing how to carry out distributionally robust optimiza- tion (DRO) for submodular functions, pro- viding efficient algorithms backed by theoret- ical guarantees which leverage several novel contributions to the general theory of DRO. We also show compelling empirical evidence that DRO improves generalization to the un- known stochastic submodular function. 

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