text: 482,19,1189246252267003907,374233623,Shane Barratt,"Excited to release our new paper ""Minimizing a Sum of Clipped Convex Functions"", joint work w/ @GuilleAngeris and Stephen Boyd. Paper: <LINK> Code: <LINK> @GuilleAngeris The paper provides a good heuristic for minimizing sums of clipped convex functions, as well as a computational lower bound based on the perspective transform. The figure below gives a simple 1-d example of a sum of clipped convex functions. <LINK> @GuilleAngeris Applications include clipped empirical risk minimization, for example, clipped regression <LINK> @GuilleAngeris And clipped control, where, for example, the cost encourages us to be in one of the two lanes <LINK> @GuilleAngeris Our algorithm requires solving roughly 5-20 convex optimization problems, and we have implemented it as a CVXPY extension, making it easy to (approximately) solve such problems <LINK> @GuilleAngeris To get a lower bound, we first convert the problem into a mixed-integer convex program using the perspective formulation (<LINK>) and relax the integral constraint to get a lower bound. (See the paper for more details.) Here is an example of the lower bound. <LINK>",https://arxiv.org/abs/1910.12342,"We consider the problem of minimizing a sum of clipped convex functions; applications include clipped empirical risk minimization and clipped control. While the problem of minimizing the sum of clipped convex functions is NP-hard, we present some heuristics for approximately solving instances of these problems. These heuristics can be used to find good, if not global, solutions and appear to work well in practice. We also describe an alternative formulation, based on the perspective transformation, which makes the problem amenable to mixed-integer convex programming and yields computationally tractable lower bounds. We illustrate one of our heuristic methods by applying it to various examples and use the perspective transformation to certify that the solutions are relatively close to the global optimum. This paper is accompanied by an open-source implementation. ",Minimizing a Sum of Clipped Convex Functions,6,"['Excited to release our new paper ""Minimizing a Sum of Clipped Convex Functions"", joint work w/ @GuilleAngeris and Stephen Boyd.\n\nPaper: <LINK>\nCode: <LINK>', '@GuilleAngeris The paper provides a good heuristic for minimizing sums of clipped convex functions, as well as a computational lower bound based on the perspective transform. The figure below gives a simple 1-d example of a sum of clipped convex functions. https://t.co/Xm6NF4BSUX', '@GuilleAngeris Applications include clipped empirical risk minimization, for example, clipped regression https://t.co/dT9PbGj3ZE', '@GuilleAngeris And clipped control, where, for example, the cost encourages us to be in one of the two lanes https://t.co/Dc5L8iTpkv', '@GuilleAngeris Our algorithm requires solving roughly 5-20 convex optimization problems, and we have implemented it as a CVXPY extension, making it easy to (approximately) solve such problems https://t.co/n3azp19CWs', '@GuilleAngeris To get a lower bound, we first convert the problem into a mixed-integer convex program using the perspective formulation (https://t.co/JKaDSTMzJT) and relax the integral constraint to get a lower bound.\n(See the paper for more details.) Here is an example of the lower bound. https://t.co/y4moDiDO4N']",19,10,1126