Results 1  10
of
152
Online passiveaggressive algorithms
 JMLR
, 2006
"... We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the nonrealizable case. The end result is new alg ..."
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Cited by 293 (22 self)
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We present a unified view for online classification, regression, and uniclass problems. This view leads to a single algorithmic framework for the three problems. We prove worst case loss bounds for various algorithms for both the realizable case and the nonrealizable case. The end result is new algorithms and accompanying loss bounds for hingeloss regression and uniclass. We also get refined loss bounds for previously studied classification algorithms. 1
Logarithmic regret algorithms for online convex optimization
 In 19’th COLT
, 2006
"... Abstract. In an online convex optimization problem a decisionmaker makes a sequence of decisions, i.e., choose a sequence of points in Euclidean space, from a fixed feasible set. After each point is chosen, it encounters an sequence of (possibly unrelated) convex cost functions. Zinkevich [Zin03] i ..."
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Cited by 123 (26 self)
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Abstract. In an online convex optimization problem a decisionmaker makes a sequence of decisions, i.e., choose a sequence of points in Euclidean space, from a fixed feasible set. After each point is chosen, it encounters an sequence of (possibly unrelated) convex cost functions. Zinkevich [Zin03] introduced this framework, which models many natural repeated decisionmaking problems and generalizes many existing problems such as Prediction from Expert Advice and Cover’s Universal Portfolios. Zinkevich showed that a simple online gradient descent algorithm achieves additive regret O ( √ T), for an arbitrary sequence of T convex cost functions (of bounded gradients), with respect to the best single decision in hindsight. In this paper, we give algorithms that achieve regret O(log(T)) for an arbitrary sequence of strictly convex functions (with bounded first and second derivatives). This mirrors what has been done for the special cases of prediction from expert advice by Kivinen and Warmuth [KW99], and Universal Portfolios by Cover [Cov91]. We propose several algorithms achieving logarithmic regret, which besides being more general are also much more efficient to implement. The main new ideas give rise to an efficient algorithm based on the Newton method for optimization, a new tool in the field. Our analysis shows a surprising connection to followtheleader method, and builds on the recent work of Agarwal and Hazan [AH05]. We also analyze other algorithms, which tie together several different previous approaches including followtheleader, exponential weighting, Cover’s algorithm and gradient descent. 1
Nearly tight bounds for the continuumarmed bandit problem
 Advances in Neural Information Processing Systems 17
, 2005
"... In the multiarmed bandit problem, an online algorithm must choose from a set of strategies in a sequence of n trials so as to minimize the total cost of the chosen strategies. While nearly tight upper and lower bounds are known in the case when the strategy set is finite, much less is known when th ..."
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Cited by 69 (4 self)
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In the multiarmed bandit problem, an online algorithm must choose from a set of strategies in a sequence of n trials so as to minimize the total cost of the chosen strategies. While nearly tight upper and lower bounds are known in the case when the strategy set is finite, much less is known when there is an infinite strategy set. Here we consider the case when the set of strategies is a subset of R d, and the cost functions are continuous. In the d = 1 case, we improve on the bestknown upper and lower bounds, closing the gap to a sublogarithmic factor. We also consider the case where d> 1 and the cost functions are convex, adapting a recent online convex optimization algorithm of Zinkevich to the sparser feedback model of the multiarmed bandit problem. 1
Convergence and noregret in multiagent learning
 In Advances in Neural Information Processing Systems 17
, 2005
"... Learning in a multiagent system is a challenging problem due to two key factors. First, if other agents are simultaneously learning then the environment is no longer stationary, thus undermining convergence guarantees. Second, learning is often susceptible to deception, where the other agents may be ..."
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Cited by 66 (0 self)
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Learning in a multiagent system is a challenging problem due to two key factors. First, if other agents are simultaneously learning then the environment is no longer stationary, thus undermining convergence guarantees. Second, learning is often susceptible to deception, where the other agents may be able to exploit a learner’s particular dynamics. In the worst case, this could result in poorer performance than if the agent was not learning at all. These challenges are identifiable in the two most common evaluation criteria for multiagent learning algorithms: convergence and regret. Algorithms focusing on convergence or regret in isolation are numerous. In this paper, we seek to address both criteria in a single algorithm by introducing GIGAWoLF, a learning algorithm for normalform games. We prove the algorithm guarantees at most zero average regret, while demonstrating the algorithm converges in many situations of selfplay. We prove convergence in a limited setting and give empirical results in a wider variety of situations. These results also suggest a third new learning criterion combining convergence and regret, which we call negative nonconvergence regret (NNR). 1
Dual averaging methods for regularized stochastic learning and online optimization
 In Advances in Neural Information Processing Systems 23
, 2009
"... We consider regularized stochastic learning and online optimization problems, where the objective function is the sum of two convex terms: one is the loss function of the learning task, and the other is a simple regularization term such as ℓ1norm for promoting sparsity. We develop extensions of Nes ..."
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Cited by 60 (3 self)
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We consider regularized stochastic learning and online optimization problems, where the objective function is the sum of two convex terms: one is the loss function of the learning task, and the other is a simple regularization term such as ℓ1norm for promoting sparsity. We develop extensions of Nesterov’s dual averaging method, that can exploit the regularization structure in an online setting. At each iteration of these methods, the learning variables are adjusted by solving a simple minimization problem that involves the running average of all past subgradients of the loss function and the whole regularization term, not just its subgradient. In the case of ℓ1regularization, our method is particularly effective in obtaining sparse solutions. We show that these methods achieve the optimal convergence rates or regret bounds that are standard in the literature on stochastic and online convex optimization. For stochastic learning problems in which the loss functions have Lipschitz continuous gradients, we also present an accelerated version of the dual averaging method.
Sparse Online Learning via Truncated Gradient
"... We propose a general method called truncated gradient to induce sparsity in the weights of onlinelearning algorithms with convex loss. This method has several essential properties. First, the degree of sparsity is continuous—a parameter controls the rate of sparsification from no sparsification to ..."
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Cited by 59 (1 self)
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We propose a general method called truncated gradient to induce sparsity in the weights of onlinelearning algorithms with convex loss. This method has several essential properties. First, the degree of sparsity is continuous—a parameter controls the rate of sparsification from no sparsification to total sparsification. Second, the approach is theoretically motivated, and an instance of it can be regarded as an online counterpart of the popular L1regularization method in the batch setting. We prove small rates of sparsification result in only small additional regret with respect to typical onlinelearning guarantees. Finally, the approach works well empirically. We apply it to several datasets and find for datasets with large numbers of features, substantial sparsity is discoverable. 1
The multiplicative weights update method: a meta algorithm and applications
, 2005
"... Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies ..."
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Cited by 53 (10 self)
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Algorithms in varied fields use the idea of maintaining a distribution over a certain set and use the multiplicative update rule to iteratively change these weights. Their analysis are usually very similar and rely on an exponential potential function. We present a simple meta algorithm that unifies these disparate algorithms and drives them as simple instantiations of the meta algorithm. 1
Robbing the Bandit: Less Regret in Online Geometric Optimization Against an Adaptive Adversary
 In Proceedings of the 17th ACMSIAM Symposium on Discrete Algorithms (SODA
, 2006
"... We consider “online bandit geometric optimization, ” a problem of iterated decision making in a largely unknown and constantly changing environment. The goal is to minimize “regret, ” defined as the difference between the actual loss of an online decisionmaking procedure and that of the best single ..."
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Cited by 47 (5 self)
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We consider “online bandit geometric optimization, ” a problem of iterated decision making in a largely unknown and constantly changing environment. The goal is to minimize “regret, ” defined as the difference between the actual loss of an online decisionmaking procedure and that of the best single decision in hindsight. “Geometric optimization ” refers to a generalization of the wellknown multiarmed bandit problem, in which the decision space is some bounded subset of R d, the adversary is restricted to linear loss functions, and regret bounds should depend on the dimensionality d, rather than the total number of possible decisions. “Bandit ” refers to the setting in which the algorithm is only told its loss on each round, rather than the entire loss function. McMahan and Blum [10] presented the best known algorithm in this setting, and proved that its expected additive regret is O(poly(d)T 3/4). We simplify and improve their analysis of this algorithm to obtain regret O(poly(d)T 2/3). We also prove that, for a large class of fullinformation online optimization problems, the optimal regret against an adaptive adversary is the same as against a nonadaptive adversary. 1
Routing without regret: On convergence to nash equilibria of regretminimizing algorithms in routing games
 In PODC
, 2006
"... Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging envi ..."
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Cited by 47 (6 self)
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Abstract There has been substantial work developing simple, efficient noregret algorithms for a wideclass of repeated decisionmaking problems including online routing. These are adaptive strategies an individual can use that give strong guarantees on performance even in adversariallychanging environments. There has also been substantial work on analyzing properties of Nash equilibria in routing games. In this paper, we consider the question: if each player in a routing game uses a noregret strategy, will behavior converge to a Nash equilibrium? In general games the answer to this question is known to be no in a strong sense, but routing games havesubstantially more structure. In this paper we show that in the Wardrop setting of multicommodity flow and infinitesimalagents, behavior will approach Nash equilibrium (formally, on most days, the cost of the flow will be close to the cost of the cheapest paths possible given that flow) at a rate that dependspolynomially on the players ' regret bounds and the maximum slope of any latency function. We also show that priceofanarchy results may be applied to these approximate equilibria, and alsoconsider the finitesize (noninfinitesimal) loadbalancing model of Azar [2].