Related papers: The Risk Quadrangle in Optimization: An Overview w…
We present a probabilistic formulation of risk aware optimal control problems for stochastic differential equations. Risk awareness is in our framework captured by objective functions in which the risk neutral expectation is replaced by a…
We provide a new algorithm for solving Risk Sensitive Partially Observable Markov Decisions Processes, when the risk is modeled by a utility function, and both the state space and the space of observations is finite. This algorithm is based…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
We introduce a new quantum R\'enyi divergence $D^{\#}_{\alpha}$ for $\alpha \in (1,\infty)$ defined in terms of a convex optimization program. This divergence has several desirable computational and operational properties such as an…
The classical theory of reinforcement learning (RL) has focused on tabular and linear representations of value functions. Further progress hinges on combining RL with modern function approximators such as kernel functions and deep neural…
Clinical risk prediction is a valuable tool for guiding healthcare interventions toward those most likely to benefit. Yet, evaluating the pairing of a risk prediction model with an intervention using randomized controlled trials presents…
We develop a deep reinforcement learning framework for dynamic portfolio optimization that combines a Dirichlet policy with cross-sectional attention mechanisms. The Dirichlet formulation ensures that portfolio weights are always feasible,…
Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating…
The dual formulation of empirical risk minimization with f-divergence regularization (ERM-fDR) is introduced. The solution of the dual optimization problem to the ERM-fDR is connected to the notion of normalization function introduced as an…
Quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…
Organizations investing in artificial intelligence face a fundamental challenge: traditional return on investment calculations fail to capture the dual nature of AI implementations, which simultaneously reduce certain operational risks…
In this paper the method of simulated quantiles (MSQ) of Dominicy and Veredas (2013) and Dominick et al. (2013) is extended to a general multivariate framework (MMSQ) and to provide a sparse estimator of the scale matrix (sparse-MMSQ). The…
Our focus is on robust recovery algorithms in statistical linear inverse problem. We consider two recovery routines - the much studied linear estimate originating from Kuks and Olman [42] and polyhedral estimate introduced in [37]. It was…
This paper introduces a novel data-driven approach to design a linear quadratic regulator (LQR) using a reinforcement learning (RL) algorithm that does not require a system model. The key contribution is to perform policy iteration (PI) by…
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…
Linear dynamical systems that obey stochastic differential equations are canonical models. While optimal control of known systems has a rich literature, the problem is technically hard under model uncertainty and there are hardly any…
Q-learning methods represent a commonly used class of algorithms in reinforcement learning: they are generally efficient and simple, and can be combined readily with function approximators for deep reinforcement learning (RL). However, the…
Stock portfolio optimization is the process of continuous reallocation of funds to a selection of stocks. This is a particularly well-suited problem for reinforcement learning, as daily rewards are compounding and objective functions may…
The key concepts (calibration, discrimination, and discordance) important in understanding and comparing risk models are best conveyed graphically. To illustrate this, models predicting death and acute kidney injury in a large cohort of PCI…