Related papers: Optimal Learning under Robustness and Time-Consist…
We study the design of information acquisition games-environments where a designer contracts their action on Sender's choice of experiment and the realized signals about some state-and identify which predictions can be made absent knowledge…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
We consider the problem of sequentially making decisions that are rewarded by "successes" and "failures" which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance.…
We study solutions of a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We…
This paper presents a partial differential equation framework for deep residual neural networks and for the associated learning problem. This is done by carrying out the continuum limits of neural networks with respect to width and depth.…
Reinforcement learning can greatly benefit from the use of options as a way of encoding recurring behaviours and to foster exploration. An important open problem is how can an agent autonomously learn useful options when solving particular…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under \textit{limited commitment}, where the seller offers a price \textit{each period} to maximize…
Given a standard Brownian motion $B^{\mu}=(B_t^{\mu})_{0\le t\le T}$ with drift $\mu \in \mathbb{R}$ and letting $S_t^{\mu}=\max_{0\le s\le t}B_s^{\mu}$ for $0\le t\le T$, we consider the optimal prediction problem: \[V=\inf_{0\le \tau \le…
The fragility of deep neural networks to adversarially-chosen inputs has motivated the need to revisit deep learning algorithms. Including adversarial examples during training is a popular defense mechanism against adversarial attacks. This…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
Robustness and safety are critical for the trustworthy deployment of deep reinforcement learning. Real-world decision making applications require algorithms that can guarantee robust performance and safety in the presence of general…
We study the problem of stopping a Brownian motion at a given distribution $\nu$ while optimizing a reward function that depends on the (possibly randomized) stopping time and the Brownian motion. Our first result establishes that the set…
We study the problem of improving the performance of online algorithms by incorporating machine-learned predictions. The goal is to design algorithms that are both consistent and robust, meaning that the algorithm performs well when…
We consider active learning under incentive compatibility constraints. The main application of our results is to economic experiments, in which a learner seeks to infer the parameters of a subject's preferences: for example their attitudes…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
This paper re-examines the use of response time to infer problem complexity. It revisits a canonical Wald model of optimal stopping, taking signal-to-noise ratio as a measure of problem complexity. While choice quality is monotone in…
We investigate the impact of Knightian uncertainty on the optimal timing policy of an ambiguity averse decision maker in the case where the underlying factor dynamics follow a multidimensional Brownian motion and the exercise payoff depends…
We study optimal double stopping problems driven by a Brownian bridge. The objective is to maximize the expected spread between the payoffs achieved at the two stopping times. We study several cases where the solutions can be solved…
We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and…