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In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game. Algorithms that minimize (standard) regret may converge to…
Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the…
We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
Estimation of average treatment effects on the treated (ATT) is an important topic of causal inference in econometrics and statistics. This problem seems to be often treated as a simple modification or extension of that of estimating…
This work revisits optimal response-adaptive designs from a type-I error rate perspective, highlighting when and how much these allocations exacerbate type-I error rate inflation - an issue previously undocumented. We explore a range of…
We study online learning problems in which the learner has extra knowledge about the adversary's behaviour, i.e., in game-theoretic settings where opponents typically follow some no-external regret learning algorithms. Under this…
We propose a sigmoidal approximation for the value-at-risk (that we call SigVaR) and we use this approximation to tackle nonlinear programs (NLPs) with chance constraints. We prove that the approximation is conservative and that the level…
Some of the most compelling applications of online convex optimization, including online prediction and classification, are unconstrained: the natural feasible set is R^n. Existing algorithms fail to achieve sub-linear regret in this…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
Projection-free online learning has drawn increasing interest due to its efficiency in solving high-dimensional problems with complicated constraints. However, most existing projection-free online methods focus on minimizing the static…
Human learners have the natural ability to use knowledge gained in one setting for learning in a different but related setting. This ability to transfer knowledge from one task to another is essential for effective learning. In this paper,…
The estimation of Average Treatment Effect (ATE) as a causal parameter is carried out in two steps, where in the first step, the treatment and outcome are modeled to incorporate the potential confounders, and in the second step, the…
In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…
It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This…
Dynamic Treatment Regimes (DTRs) provide a systematic framework for optimizing sequential decision-making in chronic disease management, where therapies must adapt to patients' evolving clinical profiles. Inverse probability weighting (IPW)…
We study average treatment effect (ATE) estimation under complete randomization with many covariates in a design-based, finite-population framework. In randomized experiments, regression adjustment can improve precision of estimators using…
Sequential prediction problems such as imitation learning, where future observations depend on previous predictions (actions), violate the common i.i.d. assumptions made in statistical learning. This leads to poor performance in theory and…
No-regret learning dynamics ensure that a learner asymptotically achieves an average reward no worse than that of any fixed strategy. This no-regret guarantee does not determine the value of the asymptotic average reward. Indeed, it is…
This paper studies the safe reinforcement learning problem formulated as an episodic finite-horizon tabular constrained Markov decision process with an unknown transition kernel and stochastic reward and cost functions. We propose a…