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The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint…
Optimization is offered as an objective approach to resolving complex, real-world decisions involving uncertainty and conflicting interests. It drives business strategies as well as public policies and, increasingly, lies at the heart of…
The aim of this paper is to study a new methodological framework for systemic risk measures by applying deep learning method as a tool to compute the optimal strategy of capital allocations. Under this new framework, systemic risk measures…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…
Portfolio optimization has been a central problem in finance, often approached with two steps: calibrating the parameters and then solving an optimization problem. Yet, the two-step procedure sometimes encounter the "error maximization"…
In our previous paper, "A Unified Approach to Systemic Risk Measures via Acceptance Set" (\textit{Mathematical Finance, 2018}), we have introduced a general class of systemic risk measures that allow for random allocations to individual…
Group Relative Policy Optimization (GRPO) has been shown to be an effective algorithm when an accurate reward model is available. However, such a highly reliable reward model is not available in many real-world tasks. In this paper, we…
This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…
In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility…
When designing a motion planner for autonomous robots there are usually multiple objectives to be considered. However, a cost function that yields the desired trade-off between objectives is not easily obtainable. A common technique across…
Continually solving new, unsolved tasks is the key to learning diverse behaviors. Through reinforcement learning (RL), we have made massive strides towards solving tasks that have a single goal. However, in the multi-task domain, where an…
Benchmark experiments are required to test, compare, tune, and understand optimization algorithms. Ideally, benchmark problems closely reflect real-world problem behavior. Yet, real-world problems are not always readily available for…
Dealing with planning problems with both logical relations and numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
The problem for selection of appropriate assets investing composition projects such as assets rationalization plays an important role in promotion of business systems. We consider the assets investing composition plan problems subject to…
Maximizing a single submodular set function subject to a cardinality constraint is a well-studied and central topic in combinatorial optimization. However, finding a set that maximizes multiple functions at the same time is much less…
Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale empirical risk minimization setting where the number of samples…