Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical optimization problems, leading to the emergence of differentiable optimization layers that permit gradient back-propagation. However, real-world scenarios often involve large-scale datasets and numerous constraints, presenting significant challenges. Current methods for differentiating optimization problems typically rely on implicit differentiation, which necessitates costly computations on the Jacobian matrices, resulting in low efficiency. In this paper, we introduce BPQP, a differentiable convex optimization framework designed for efficient end-to-end learning. To enhance efficiency, we reformulate the backward pass as a simplified and decoupled quadratic programming problem by leveraging the structural properties of the Karush–Kuhn–Tucker (KKT) matrix. This reformulation enables the use of first-order optimization algorithms in calculating the backward pass gradients, allowing our framework to potentially utilize any state-of-the-art solver. As solver technologies evolve, BPQP can continuously adapt and improve its efficiency. Extensive experiments on both simulated and real-world datasets demonstrate that BPQP achieves a significant improvement in efficiency—typically an order of magnitude faster in overall execution time compared to other differentiable optimization layers. Our results not only highlight the efficiency gains of BPQP but also underscore its superiority over differential optimization layer baselines.

Modern graphics processing units (GPUs) are delivering tremendous computing horsepower by running tens of thousands of threads concurrently. The massively parallel execution model has been effective to hide the long latency of off-chip memory accesses in graphics and other general computing applications exhibiting regular memory behaviors. With the fast-growing demand for general purpose computing on GPUs (GPGPU), GPU workloads are becoming highly diversified, and thus requiring a synergistic coordination of both computing and memory resources to unleash the computing power of GPUs. Accordingly, recent graphics processors begin to integrate an on-die level-2 (L2) cache. The huge number of threads on GPUs, however, poses significant challenges to L2 cache design. The experiments on a variety of GPGPU applications reveal that the L2 cache may or may not improve the overall performance depending on the characteristics of applications. In this paper, we propose efficient techniques to improve GPGPU performance by orchestrating both L2 cache and memory in a unified framework. The basic philosophy is to exploit the temporal locality among the massive number of concurrent memory requests and minimize the impact of memory divergence behaviors among simultaneously executed groups of threads. Our major contributions are twofold. First, a priority-based cache management is proposed to maximize the chance of frequently revisited data to be kept in the cache. Second, an effective memory scheduling is introduced to reorder memory requests in the memory controller according to the divergence behavior for reducing average waiting time of warps. Simulation results reveal that our techniques enhance the overall performance by 10% on average for memory intensive benchmarks, whereas the maximum gain can be up to 30%.