Related papers: A Stability Principle for Learning under Non-Stati…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…
The basic question of delineating those statistical problems that are solvable without making any assumptions on the underlying data distribution has long animated statistics and learning theory. This paper characterizes when a convex…
In the last several years, the intimate connection between convex optimization and learning problems, in both statistical and sequential frameworks, has shifted the focus of algorithmic machine learning to examine this interplay. In…
We consider reinforcement learning (RL) in episodic MDPs with adversarial full-information reward feedback and unknown fixed transition kernels. We propose two model-free policy optimization algorithms, POWER and POWER++, and establish…
Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t. time and amount) changes is a challenging and largely unexplored problem of great significance. We consider the class of piecewise Lipschitz functions, which is…
We study nonparametric contextual bandits under batch constraints, where the expected reward for each action is modeled as a smooth function of covariates, and the policy updates are made at the end of each batch of observations. We…
We present a method for providing statistical guarantees on runtime safety and goal reachability for integrated planning and control of a class of systems with unknown nonlinear stochastic underactuated dynamics. Specifically, given a…
Stochastic and adversarial data are two widely studied settings in online learning. But many optimization tasks are neither i.i.d. nor fully adversarial, which makes it of fundamental interest to get a better theoretical understanding of…
We study stochastic optimization of nonconvex loss functions, which are typical objectives for training neural networks. We propose stochastic approximation algorithms which optimize a series of regularized, nonlinearized losses on large…
Extracting dynamic models from data is of enormous importance in understanding the properties of unknown systems. In this work, we employ Lipschitz neural networks, a class of neural networks with a prescribed upper bound on their Lipschitz…
We consider a general online stochastic optimization problem with multiple budget constraints over a horizon of finite time periods. In each time period, a reward function and multiple cost functions are revealed, and the decision maker…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…
In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is \emph{asymptotically} equivalent to a stochastic…
This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…
It is a known fact that not all controllable systems can be asymptotically stabilized by a continuous static feedback. Several approaches have been developed throughout the last decades, including time-varying, dynamical and even…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
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…