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We consider an online learning process to forecast a sequence of outcomes for nonconvex models. A typical measure to evaluate online learning algorithms is regret but such standard definition of regret is intractable for nonconvex models…

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses…

We derive a novel asymptotic problem-dependent lower-bound for regret minimization in finite-horizon tabular Markov Decision Processes (MDPs). While, similar to prior work (e.g., for ergodic MDPs), the lower-bound is the solution to an…

We study the dynamic regret of multi-armed bandit and experts problem in non-stationary stochastic environments. We introduce a new parameter $\Lambda$, which measures the total statistical variance of the loss distributions over $T$ rounds…

A central problem in the theory of empirical Bayes is to control the regret (excess risk) of a learned Bayes rule by the Hellinger distance between the estimated and true marginal densities. In the normal means model, the classical result…

We present new algorithms for online convex optimization over unbounded domains that obtain parameter-free regret in high-probability given access only to potentially heavy-tailed subgradient estimates. Previous work in unbounded domains…

In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…

We address the problem of the achievable regret rates with online logistic regression. We derive lower bounds with logarithmic regret under $L_1$, $L_2$, and $L_\infty$ constraints on the parameter values. The bounds are dominated by $d/2…

In the online non-stochastic control problem, an agent sequentially selects control inputs for a linear dynamical system when facing unknown and adversarially selected convex costs and disturbances. A common metric for evaluating control…

In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret…

We consider the problem of recommending relevant labels (items) for a given data point (user). In particular, we are interested in the practically important setting where the evaluation is with respect to non-decomposable (over labels)…

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…

Adaptive gradient algorithms such as ADAGRAD and its variants have gained popularity in the training of deep neural networks. While many works as for adaptive methods have focused on the static regret as a performance metric to achieve a…

Reinforcement learning (RL) has traditionally been understood from an episodic perspective; the concept of non-episodic RL, where there is no restart and therefore no reliable recovery, remains elusive. A fundamental question in…

We introduce a new online convex optimization algorithm that adaptively chooses its regularization function based on the loss functions observed so far. This is in contrast to previous algorithms that use a fixed regularization function…

We consider the fixed-budget best arm identification problem with rewards following normal distributions. In this problem, the forecaster is given $K$ arms (or treatments) and $T$ time steps. The forecaster attempts to find the arm with the…

The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks. It is common belief that the optimizer dynamics, network…

In this paper, we address tracking of a time-varying parameter with unknown dynamics. We formalize the problem as an instance of online optimization in a dynamic setting. Using online gradient descent, we propose a method that sequentially…

We consider the problem of the Zinkevich (2003)-style dynamic regret minimization in online learning with exp-concave losses. We show that whenever improper learning is allowed, a Strongly Adaptive online learner achieves the dynamic regret…

We consider a generalization of the celebrated Online Convex Optimization (OCO) framework with adversarial online constraints. In this problem, an online learner interacts with an adversary sequentially over multiple rounds. At the…