We study the fundamental mistake bound and sample complexity in the strategic1 classification, where agents can strategically manipulate their feature vector up2 to an extent in order to be predicted as positive. For example, given a classifier3 determining college admission, student candidates may try to take easier classes to4 improve their GPA, retake SAT and change schools in an effort to fool the classifier.5 Ball manipulations are a widely studied class of manipulations in the literature,6 where agents can modify their feature vector within a bounded radius ball. Unlike7 most prior work, our work consider manipulations to be personalized, meaning8 that agents can have different levels of manipulation abilities (e.g., varying radii9 for ball manipulations), and unknown to the learner.10 We formalize the learning problem in an interaction model where the learner11 first deploys a classifier and the agent manipulates the feature vector within their12 manipulation set to game the deployed classifier. We investigate various scenarios13 in terms of the information available to the learner during the interaction, such14 as observing the original feature vector before or after deployment, observing the15 manipulated feature vector, or not seeing either the original or the manipulated16 feature vector. We begin by providing online mistake bounds and PAC sample17 complexity in these scenarios for ball manipulations. We also explore non-ball18 manipulations and show that, even in the simplest scenario where both the original19 and the manipulated feature vectors are revealed, the mistake bounds and sample20 complexity are lower bounded by Ω(|H|) when the target function belongs to a21 known class H.22

Givenanincoming stream ofvideoframes, online action detection [14]isconcerned withthetask of classifying what is happening at each frame without seeing the future.

Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems such as reasoning in a nonmonotonic setting can be directly formulated in ASP. Although the main problems of ASP are of high computational complexity, located at the second level of the Polynomial Hierarchy, several restrictions of ASP have been identified in the literature, under which ASP problems become tractable. In this paper we use the concept of backdoors to identify new restrictions that make ASP problems tractable. Small backdoors are sets of atoms that represent "clever reasoning shortcuts" through the search space and represent a hidden structure in the problem input. The concept of backdoors is widely used in the areas of propositional satisfiability and constraint satisfaction. We show that it can be fruitfully adapted to ASP. We demonstrate how backdoors can serve as a unifying framework that accommodates several tractable restrictions of ASP known from the literature. Furthermore, we show how backdoors allow us to deploy recent algorithmic results from parameterized complexity theory to the domain of answer set programming.