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For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\lambda\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control…
The contextual bandit literature has traditionally focused on algorithms that address the exploration-exploitation tradeoff. In particular, greedy algorithms that exploit current estimates without any exploration may be sub-optimal in…
In this study, a nondominated-solution-based multi-objective greedy method is proposed and applied to a sensor selection problem based on the multiple indices of the optimal design of experiments. The proposed method simultaneously…
We study influence maximization on temporal networks. This is a special setting where the influence function is not submodular, and there is no optimality guarantee for solutions achieved via greedy optimization. We perform an exhaustive…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
We study a fundamental problem in Bayesian learning, where the goal is to select a set of data sources with minimum cost while achieving a certain learning performance based on the data streams provided by the selected data sources. First,…
This thesis investigates Merton's portfolio problem under two different rough Heston models, which have a non-Markovian structure. The motivation behind this choice of problem is due to the recent discovery and success of rough volatility…
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…
We study adaptive combinatorial maximization, which is a core challenge in machine learning, with applications in active learning as well as many other domains. We study the Bayesian setting, and consider the objectives of maximization…
We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also…
Consider the puzzle: given a number, remove $k$ digits such that the resulting number is as large as possible. Various techniques were employed to derive a linear-time solution to the puzzle: predicate logic was used to justify the…
The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a "good definition" of admissible strategies, so that an…
We consider a discrete-time, generically incomplete market model and a behavioural investor with power-like utility and distortion functions. The existence of optimal strategies in this setting has been shown in a previous paper under…
We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…
The main focus of this article is to provide a mathematical study of the algorithm proposed in \cite{boyaval2010variance} where the authors proposed a variance reduction technique for the computation of parameter-dependent expectations…
This paper studies a type of periodic utility maximization problems for portfolio management in incomplete stochastic factor models with convex trading constraints. The portfolio performance is periodically evaluated on the relative ratio…
We empirically analyze a simple heuristic for large sparse set cover problems. It uses the weighted greedy algorithm as a basic building block. By multiplicative updates of the weights attached to the elements, the greedy solution is…
We develop a regression based primal-dual martingale approach for solving finite time horizon MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…
Greedy algorithms are popular in compressive sensing for their high computational efficiency. But the performance of current greedy algorithms can be degenerated seriously by noise (both multiplicative noise and additive noise). A robust…