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We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Holder-smooth…
We consider a natural model of online preference aggregation, where sets of preferred items $R_1, R_2, \ldots, R_t$ along with a demand for $k_t$ items in each $R_t$, appear online. Without prior knowledge of $(R_t, k_t)$, the learner…
We present a generalization of the adversarial linear bandits framework, where the underlying losses are kernel functions (with an associated reproducing kernel Hilbert space) rather than linear functions. We study a version of the…
We prove the familiar Lazy Online Gradient Descent algorithm is universal on polytope domains. That means it gets $O(1)$ pseudo-regret against i.i.d opponents, while simultaneously achieving the well-known $O(\sqrt N)$ worst-case regret…
We present a new perspective on online learning that we refer to as gradient equilibrium: a sequence of iterates achieves gradient equilibrium if the average of gradients of losses along the sequence converges to zero. In general, this…
In this paper, we focus on the question of the extent to which online learning can benefit from distributed computing. We focus on the setting in which $N$ agents online-learn cooperatively, where each agent only has access to its own data.…
This paper introduces a novel family of generalized exponentiated gradient (EG) updates derived from an Alpha-Beta divergence regularization function. Collectively referred to as EGAB, the proposed updates belong to the category of…
Motivated by the predictable nature of real-life in data streams, we study online regression when the learner has access to predictions about future examples. In the extreme case, called transductive online learning, the sequence of…
We tackle the problem of online optimization with a general, possibly unbounded, loss function. It is well known that when the loss is bounded, the exponentially weighted aggregation strategy (EWA) leads to a regret in $\sqrt{T}$ after $T$…
Recent work across many machine learning disciplines has highlighted that standard descent methods, even without explicit regularization, do not merely minimize the training error, but also exhibit an implicit bias. This bias is typically…
We address the online linear optimization problem with bandit feedback. Our contribution is twofold. First, we provide an algorithm (based on exponential weights) with a regret of order $\sqrt{d n \log N}$ for any finite action set with $N$…
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…
We consider the setting of online logistic regression and consider the regret with respect to the 2-ball of radius B. It is known (see [Hazan et al., 2014]) that any proper algorithm which has logarithmic regret in the number of samples…
This paper investigates in depth the fundamental properties of the two-parameter generalized Euler logarithm and its inverse, the associated deformed $(a,b)$-exponential function. We systematically clarify the parameter domains that…
In this paper, we consider an online distributed composite optimization problem over a time-varying multi-agent network that consists of multiple interacting nodes, where the objective function of each node consists of two parts: a loss…
Evolutionary Strategies (ES) are known to be an effective black-box optimization technique for deep neural networks when the true gradients cannot be computed, such as in Reinforcement Learning. We continue a recent line of research that…
The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine…
This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to…
We present a new online learning algorithm for cumulative discounted gain. This learning algorithm does not use exponential weights on the experts. Instead, it uses a weighting scheme that depends on the regret of the master algorithm…
We consider prediction with expert advice when the loss vectors are assumed to lie in a set described by the sum of atomic norm balls. We derive a regret bound for a general version of the online mirror descent (OMD) algorithm that uses a…