Learning with a Drifting Target Concept

We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates

The Power of Localization for Efficiently Learning Linear Separators with Noise

We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model and the adversarial label noise model. For malicious noise, where the adversary can corrupt both the label and the features, we provide a polynomial-time algorithm for learning linear separators in $\Re^d$ under isotropic log-concave distributions that can tolerate a nearly information-theoretically optimal noise rate of $\eta = \Omega(\epsilon)$. For the adversarial label noise model, where the distribution over the feature vectors is unchanged, and the overall probability of a noisy label is constrained to be at most $\eta$, we also give a polynomial-time algorithm for learning linear separators in $\Re^d$ under isotropic log-concave distributions that can handle a noise rate of $\eta = \Omega\left(\epsilon\right)$. We show that, in the active learning model, our algorithms achieve a label complexity whose dependence on the error parameter $\epsilon$ is polylogarithmic. This provides the first polynomial-time active learning algorithm for learning linear separators in the presence of malicious noise or adversarial label noise.Comment: Contains improved label complexity analysis communicated to us by Steve Hannek

An Adaptive Algorithm for Learning with Unknown Distribution Drift

We develop and analyze a general technique for learning with an unknown distribution drift. Given a sequence of independent observations from the last $T$ steps of a drifting distribution, our algorithm agnostically learns a family of functions with respect to the current distribution at time $T$. Unlike previous work, our technique does not require prior knowledge about the magnitude of the drift. Instead, the algorithm adapts to the sample data. Without explicitly estimating the drift, the algorithm learns a family of functions with almost the same error as a learning algorithm that knows the magnitude of the drift in advance. Furthermore, since our algorithm adapts to the data, it can guarantee a better learning error than an algorithm that relies on loose bounds on the drift.Comment: Fixed typos and references. Updated conclusio

A Stability Principle for Learning under Non-Stationarity

We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while keeping the cumulative bias within an acceptable range relative to the stochastic error. Our theory showcases the adaptability of this approach to unknown non-stationarity. The regret bound is minimax optimal up to logarithmic factors when the population losses are strongly convex, or Lipschitz only. At the heart of our analysis lie two novel components: a measure of similarity between functions and a segmentation technique for dividing the non-stationary data sequence into quasi-stationary pieces.Comment: 47 pages, 1 figur