Effective exploration is believed to positively influence the long-term user experience on recommendation platforms. Determining its exact benefits, however, has been challenging. Regular A/B tests on exploration often measure neutral or even negative engagement metrics while failing to capture its long-term benefits. We here introduce new experiment designs to formally quantify the long-term value of exploration by examining its effects on content corpus, and connecting content corpus growth to the long-term user experience from real-world experiments. Once established the values of exploration, we investigate the Neural Linear Bandit algorithm as a general framework to introduce exploration into any deep learning based ranking systems. We conduct live experiments on one of the largest short-form video recommendation platforms that serves billions of users to validate the new experiment designs, quantify the long-term values of exploration, and to verify the effectiveness of the adopted neural linear bandit algorithm for exploration.

Recommendation system serves as a conduit connecting users to an incredibly large, diverse and ever growing collection of contents. In practice, missing information on fresh (and tail) contents needs to be filled in order for them to be exposed and discovered by their audience. We here share our success stories in building a dedicated fresh content recommendation stack on a large commercial platform. To nominate fresh contents, we built a multi-funnel nomination system that combines (i) a two-tower model with strong generalization power for coverage, and (ii) a sequence model with near real-time update on user feedback for relevance. The multi-funnel setup effectively balances between coverage and relevance. An in-depth study uncovers the relationship between user activity level and their proximity toward fresh contents, which further motivates a contextual multi-funnel setup. Nominated fresh candidates are then scored and ranked by systems considering prediction uncertainty to further bootstrap content with less exposure. We evaluate the benefits of the dedicated fresh content recommendation stack, and the multi-funnel nomination system in particular, through user corpus co-diverted live experiments. We conduct multiple rounds of live experiments on a commercial platform serving billion of users demonstrating efficacy of our proposed methods.

Abstract—Communication-optimal algorithms are known for square matrix multiplication. Here, we obtain the first communication-optimal algorithm for all dimensions of rectangular matrices. Combining the dimension-splitting technique of Frigo, Leiserson, Prokop and Ramachandran (1999) with the recursive BFS/DFS approach of Ballard, Demmel, Holtz, Lipshitz and Schwartz (2012) allows for a communication-optimal as well as cache- and network-oblivious algorithm. Moreover, the implementation is simple: approximately 50 lines of code for the shared-memory version. Since the new algorithm minimizes communication across the network, between NUMA domains, and between levels of cache, it performs well in practice on both shared- and distributed-memory machines. We show significant speedups over existing parallel linear algebra libraries both on a 32-core shared-memory machine and on a distributed-memory supercomputer. Index Terms—communication-avoiding algorithms; linear algebra; matrix multiplication I.

Energy efficiency of computing devices has become a dominant area of research interest in recent years. Most previous work has focused on architectural techniques to improve power and energy efficiency; only a few consider saving energy at the algorithmic level. We prove that a region of perfect strong scaling in energy exists for matrix multiplication (classical and Strassen) and the direct n-body problem via the use of algorithms that use all available memory to replicate data. This means that we can increase the number of processors by some factor and decrease the runtime (both computation and communication) by the same factor, without changing the total energy use.

Parallel algorithms for sparse matrix-matrix multiplication typically spend most of their time on inter-processor communication rather than on computation, and hardware trends predict the relative cost of communication will only increase. Thus, sparse matrix multiplication algorithms must minimize communication costs in order to scale to large processor counts.

High performance for numerical linear algebra often comes at the expense of stability. Computing the LU decomposition of a matrix via Gaussian Elimination can be organized so that the computation involves regular and efficient data access. However, maintaining numerical stability via partial pivoting involves row interchanges that lead to inefficient data access patterns. To optimize communication efficiency throughout the memory hierarchy we confront two seemingly contradictory requirements: partial pivoting is efficient with column-major layout, whereas a block-recursive layout is optimal for the rest of the computation. We resolve this by introducing a shape morphing procedure that dynamically matches the layout to the computation throughout the algorithm, and show that Gaussian Elimination with partial pivoting can be performed in a communication efficient and cache-oblivious way. Our technique extends to QR decomposition, where computing Householder vectors prefers a different data layout than the rest of the computation.

Matrix multiplication is a fundamental kernel of many high performance and scientific computing applications. Most parallel implementations use classical O(n3) matrix multiplication, even though there exist algorithms with lower arithmetic complexity. We recently presented a new Communication-Avoiding Parallel Strassen algorithm (CAPS), based on Strassen's fast matrix multiplication, that minimizes communication (SPAA'12). It communicates asymptotically less than all classical and all previous Strassen-based algorithms, and it attains theoretical lower bounds. In this paper we show that CAPS is also faster in practice. We benchmark and compare its performance to previous algorithms on Hopper (Cray XE6), Intrepid (IBM BG/P), and Franklin (Cray XT4). We demonstrate significant speedups over previous algorithms both for large matrices and for small matrices on large numbers of processors. We model and analyze the performance of CAPS and predict its performance on future exascale platforms.

A parallel algorithm has perfect strong scaling if its running time on $P$ processors is linear in $1/P$, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only recently been found. One is based on classical matrix multiplication (Solomonik and Demmel, 2011), and one is based on Strassen's fast matrix multiplication (Ballard, Demmel, Holtz, Lipshitz, and Schwartz, 2012). Both algorithms scale perfectly, but only up to some number of processors where the inter-processor communication no longer scales. We obtain a memory-independent communication cost lower bound on classical and Strassen-based distributed-memory matrix multiplication algorithms. These bounds imply that no classical or Strassen-based parallel matrix multiplication algorithm can strongly scale perfectly beyond the ranges already attained by the two parallel algorithms mentioned above. The memory-independent bounds and the strong scaling bounds generalize to other algorithms.

Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes communication. The algorithm outperforms all known parallel matrix multiplication algorithms, classical and Strassen-based, both asymptotically and in practice. A critical bottleneck in parallelizing Strassen's algorithm is the communication between the processors. Ballard, Demmel, Holtz, and Schwartz (SPAA '11) prove lower bounds on these communication costs, using expansion properties of the underlying computation graph. Our algorithm matches these lower bounds, and so is communication-optimal. It exhibits perfect strong scaling within the maximum possible range.