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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)

- H. Brendan McMahan, Gary Holt, +13 authors Jeremy Kubica
- KDD
- 2013

Predicting ad click-through rates (CTR) is a massive-scale learning problem that is central to the multi-billion dollar online advertising industry. We present a selection of case studies and topics drawn from recent experiments in the setting of a deployed CTR prediction system. These include improvements in the context of traditional supervised learning… (More)

- H. Brendan McMahan, Avrim Blum
- COLT
- 2004

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 xt S while simultaneously an adversary selects a cost vector ct… (More)

- H. Brendan McMahan, Matthew J. Streeter
- COLT
- 2010

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 such as L2-squared, and modify it only via a single time-dependent parameter. Our algorithm’s regret bounds are worst-case… (More)

- H. Brendan McMahan, Geoffrey J. Gordon, Avrim Blum
- ICML
- 2003

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)

- Martín Abadi, Andy Chu, +4 authors Li Zhang
- ACM Conference on Computer and Communications…
- 2016

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)

- H. Brendan McMahan, Matthew J. Streeter
- NIPS
- 2014

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)

- H. Brendan McMahan
- AISTATS
- 2011

We prove that many mirror descent algorithms for online convex optimization (such as online gradient descent) have an equivalent interpretation as follow-the-regularizedleader (FTRL) algorithms. This observation makes the relationships between many commonly used algorithms explicit, and provides theoretical insight on previous experimental observations. In… (More)