Active classification with comparison queries

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a specific restaurant (a label query); or which one of two restaurants did she like more (a comparison query). We focus on the class of half spaces, and show that under natural assumptions, such as large margin or bounded bit-description of the input examples, it is possible to reveal all the labels of a sample of size $n$ using approximately $O(\log n)$ queries. This implies an exponential improvement over classical active learning, where only label queries are allowed. We complement these results by showing that if any of these assumptions is removed then, in the worst case, $\Omega(n)$ queries are required. Our results follow from a new general framework of active learning with additional queries. We identify a combinatorial dimension, called the \emph{inference dimension}, that captures the query complexity when each additional query is determined by $O(1)$ examples (such as comparison queries, each of which is determined by the two compared examples). Our results for half spaces follow by bounding the inference dimension in the cases discussed above.Comment: 23 pages (not including references), 1 figure. The new version contains a minor fix in the proof of Lemma 4.

Modeling Driver Behavior From Demonstrations in Dynamic Environments Using Spatiotemporal Lattices

International audienceOne of the most challenging tasks in the development of path planners for intelligent vehicles is the design of the cost function that models the desired behavior of the vehicle. While this task has been traditionally accomplished by hand-tuning the model parameters, recent approaches propose to learn the model automatically from demonstrated driving data using Inverse Reinforcement Learning (IRL). To determine if the model has correctly captured the demonstrated behavior, most IRL methods require obtaining a policy by solving the forward control problem repetitively. Calculating the full policy is a costly task in continuous or large domains and thus often approximated by finding a single trajectory using traditional path-planning techniques. In this work, we propose to find such a trajectory using a conformal spatiotemporal state lattice, which offers two main advantages. First, by conforming the lattice to the environment, the search is focused only on feasible motions for the robot, saving computational power. And second, by considering time as part of the state, the trajectory is optimized with respect to the motion of the dynamic obstacles in the scene. As a consequence, the resulting trajectory can be used for the model assessment. We show how the proposed IRL framework can successfully handle highly dynamic environments by modeling the highway tactical driving task from demonstrated driving data gathered with an instrumented vehicle