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We study a general online convex optimization problem. We have a convex set <i>S</i> and an unknown sequence of cost functions <i>c</i><inf>1</inf>, <i>c</i><inf>2</inf>,..., and in each period, we choose a feasible point <i>x<inf>t</inf></i> in <i>S</i>, and learn the cost <i>c<inf>t</inf></i>(<i>x<inf>t</inf></i>). If the function <i>c<inf>t</inf></i> is(More)
In many applications, one has to actively select among a set of expensive observations before making an informed decision. For example, in environmental monitoring, we want to select locations to measure in order to most effectively predict spatial phenomena. Often, we want to select observations which are robust against a number of possible objective(More)
MDPs are an attractive formalization for planning, but realistic problems often have intractably large state spaces. When we only need a partial policy to get from a fixed start state to a goal, restricting computation to states relevant to this task can make much larger problems tractable. We introduce a new algorithm, Bounded RTDP, which can produce(More)
Machine learning techniques based on neural networks are achieving remarkable results in a wide variety of domains. Often, the training of models requires large, representative datasets, which may be crowdsourced and contain sensitive information. The models should not expose private information in these datasets. Addressing this goal, we develop new(More)
We give an algorithm for the bandit version of a very general online optimization problem considered by Kalai and Vempala [1], for the case of an adaptive adversary. In this problem we are given a bounded set S ¢ ¤ £ n of feasible points. At each time step t, the online algorithm must select a point x t ¥ S while simultaneously an adversary selects a cost(More)
We investigate methods for planning in a Markov Decision Process where the cost function is chosen by an adversary after we fix our policy. As a running example, we consider a robot path planning problem where costs are influenced by sensors that an adversary places in the environment. We formulate the problem as a zero-sum matrix game where rows correspond(More)
We prove that many mirror descent algorithms for online convex optimization (such as online gradient descent) have an equivalent interpretation as follow-the-regularized-leader (FTRL) algorithms. This observation makes the relationships between many commonly used algorithms explicit, and provides theoretical insight on previous experimental observations. In(More)
We analyze new online gradient descent algorithms for distributed systems with large delays between gradient computations and the corresponding updates. Using insights from adaptive gradient methods, we develop algorithms that adapt not only to the sequence of gradients, but also to the precise update delays that occur. We first give an impractical(More)
We study stochastic optimization problems when the data is sparse, which is in a sense dual to current perspectives on high-dimensional statistical learning and optimization. We highlight both the difficulties—in terms of increased sample complexity that sparse data necessitates—and the potential benefits, in terms of allowing parallelism and asynchrony in(More)