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We develop an online algorithm called Component Hedge for learning structured concept classes when the loss of a structured concept sums over its components. Example classes include paths through a graph (composed of edges) and partial permutations (composed of assignments). The algorithm maintains a parameter vector with one non-negative weight per… (More)

Follow-the-Leader (FTL) is an intuitive sequential prediction strategy that guarantees constant regret in the stochastic setting, but has terrible performance for worst-case data. Other hedging strategies have better worst-case guarantees but may perform much worse than FTL if the data are not maximally adversarial. We introduce the FlipFlop algorithm,… (More)

For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t 1 , t 2 ] is the loss of the algorithm minus the loss of the best expert over that interval. Adaptive regret measures how well the algorithm approximates the best expert locally,… (More)

We show how models for prediction with expert advice can be defined concisely and clearly using hidden Markov models (HMMs); standard HMM algorithms can then be used to efficiently calculate how the expert predictions should be weighted according to the model. We cast many existing models as HMMs and recover the best known running times in each case. We… (More)

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision tasks. We are not satisfied with just guaranteeing minimax regret rates, but we want our algorithms to perform significantly… (More)

We consider sequential prediction algorithms that are given the predictions from a set of models as inputs. If the nature of the data is changing over time in that different models predict well on different segments of the data, then adaptivity is typically achieved by mixing into the weights in each round a bit of the initial prior (kind of like a weak… (More)

Most standard algorithms for prediction with expert advice depend on a parameter called the learning rate. This learning rate needs to be large enough to fit the data well, but small enough to prevent overfitting. For the exponential weights algorithm , a sequence of prior work has established theoretical guarantees for higher and higher data-dependent… (More)

Performance guarantees for online learning algorithms typically take the form of regret bounds, which express that the cumulative loss overhead compared to the best expert in hindsight is small. In the common case of large but structured expert sets we typically wish to keep the regret especially small compared to simple experts, at the cost of modest… (More)

We propose a new way to build a combined list from K base lists, each containing N items. A combined list consists of top segments of various sizes from each base list so that the total size of all top segments equals N. A sequence of item requests is processed and the goal is to minimize the total number of misses. That is, we seek to build a combined list… (More)