Gaussian entries, thegoal isto recover thek-sparse unit vectorx Rn. The structure we enforce on x is sparsity: |supp(x)| k.

We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue fromtheseller side.

Differentiable Architecture Search (DARTS) is a recently proposed neural architecture search (NAS) method based on a differentiable relaxation. Due to its success, numerous variants analyzing and improving parts of the DARTS framework have recently been proposed. By considering the problem as a constrained bilevel optimization, we propose and analyze three improvements to architectural weight competition, update scheduling, and regularization towards discretization. First, we introduce a new approach to the activation of architecture weights, which prevents confounding competition within an edge and allows for fair comparison across edges to aid in discretization. Next, we propose a dynamic schedule based on per-minibatch network information to make architecture updates more informed. Finally, we consider two regularizations, based on proximity to discretization and the Alternating Directions Method of Multipliers (ADMM) algorithm, to promote early discretization. Our results show that this new activation scheme reduces final architecture size and the regularizations improve reliability in search results while maintaining comparable performance to state-of-the-art in NAS, especially when used with our new dynamic informed schedule.

The work presented in this report introduces a framework aimed towards learning to imitate human gaits. Humans exhibit movements like walking, running, and jumping in the most efficient manner, which served as the source of motivation for this project. Skeletal and Musculoskeletal human models were considered for motions in the sagittal plane, and results from both were compared exhaustively. While skeletal models are driven with motor actuation, musculoskeletal models perform through muscle-tendon actuation. Model-free reinforcement learning algorithms were used to optimize inverse dynamics control actions to satisfy the objective of imitating a reference motion along with secondary objectives of minimizing effort in terms of power spent by motors and metabolic energy consumed by the muscles. On the one hand, the control actions for the motor actuated model is the target joint angles converted into joint torques through a Proportional-Differential controller. While on the other hand, the control actions for the muscle-tendon actuated model is the muscle excitations converted implicitly to muscle activations and then to muscle forces which apply moments on joints. Muscle-tendon actuated models were found to have superiority over motor actuation as they are inherently smooth due to muscle activation dynamics and don't need any external regularizers. Finally, a strategy that was used to obtain an optimal configuration of the significant decision variables in the framework was discussed. All the results and analysis are presented in an illustrative, qualitative, and quantitative manner. Supporting video links are provided in the Appendix.