We present an algorithm for learning switched linear dynamical systems in discrete time from noisy observations of the system's full state or output. Switched linear systems use multiple linear dynamical modes to fit the data within some desired tolerance. They arise quite naturally in applications to robotics and cyberphysical systems. Learning switched systems from data is a NP-hard problem that is nearly identical to the k-linear regression problem of fitting k > 1 linear models to the data. A direct mixed-integer linear programming (MILP) approach yields time complexity that is exponential in the number of data points. In this paper, we modify the problem formulation to yield an algorithm that is linear in the size of the data while remaining exponential in the number of state variables and the desired number of modes. To do so, we combine classic ideas from the ellipsoidal method for solving convex optimization problems, and well-known oracle separation results in non-smooth optimization. We demonstrate our approach on a set of microbenchmarks and a few interesting real-world problems. Our evaluation suggests that the benefits of this algorithm can be made practical even against highly optimized off-the-shelf MILP solvers.

Google has enhanced its'Results About You' privacy tool to help users monitor and remove personal information like government ID numbers from search results, according to PCWorld. The update includes a streamlined process for removing explicit images through a three-dot menu option and allows bulk removal requests. These privacy improvements are rolling out in the US first as part of Google's Safer Internet Day initiatives, giving users better control over their digital footprint. In celebration of Safer Internet Day, Google rolled out an update to its "Results About You" feature and launched a new, simpler tool for removing unwanted explicit images from search results. With Results About You, you can tell Google to keep track of search results where your personal information appears, and then ask Google to remove those search results. The feature has previously been able to track search results with your home address, email address, and phone number, but now the search engine will also be able to warn you about search results that include your government documents, such as passports or driver's licenses. The update to Results About You will first be rolled out in the United States over the coming days, but Google is working on adapting the feature for other regions as well.

People have a right to know who their neighbors are, especially when it's ICE. On Tuesday, WIRED published details of ICE's planned expansion into more than 150 office spaces across the United States, including 54 specific addresses. ICE has designs on every major US city. It plans to not only occupy existing government spaces but share hallways and elevator bays with medical offices and small businesses. It will be down the street from daycares and within walking distance of churches and treatment centers.

We establish upper bounds on the regrets of the problem with respect to time horizon, manifold curvature, and manifold dimension.

Assume the conditions in Proposition 1 hold.

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