Related papers: Risk-Adaptive Approaches to Stochastic Optimizatio…
A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…
We develop a tractable and flexible approach for incorporating side information into dynamic optimization under uncertainty. The proposed framework uses predictive machine learning methods (such as $k$-nearest neighbors, kernel regression,…
Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic…
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…
Energy infrastructure planning under uncertainty has become increasingly complex as electrification, interdependence between energy carriers, decarbonization, and extreme weather events reshape long-term investment decisions. This paper…
The financial crisis has dramatically demonstrated that the traditional approach to apply univariate monetary risk measures to single institutions does not capture sufficiently the perilous systemic risk that is generated by the…
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…
We introduce set risk measures (SRMs), real-valued maps defined on the family of non-empty closed bounded sets of essentially bounded random variables. SRMs extend traditional scalar risk measures by assigning a single capital requirement…
Fair predictive algorithms hinge on both equality and trust, yet inherent uncertainty in real-world data challenges our ability to make consistent, fair, and calibrated decisions. While fairly managing predictive error has been extensively…
We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…
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…
We develop a framework for interacting with uncertain environments in reinforcement learning (RL) by leveraging preferences in the form of utility functions. We claim that there is value in considering different risk measures during…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
Advanced classification algorithms are being increasingly used in safety-critical applications like health-care, engineering, etc. In such applications, miss-classifications made by ML algorithms can result in substantial financial or…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
We consider a task of scheduling with a common deadline on a single machine. Every player reports to a scheduler the length of his job and the scheduler needs to finish as many jobs as possible by the deadline. For this simple problem,…
Risk scores are simple classification models that let users make quick risk predictions by adding and subtracting a few small numbers. These models are widely used in medicine and criminal justice, but are difficult to learn from data…
We study the effect of stochasticity in on-policy policy optimization, and make the following four contributions. First, we show that the preferability of optimization methods depends critically on whether stochastic versus exact gradients…
Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…