Song Yao

Erhan Bayraktar, Song Yao

We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from $\cP$. We show that the \emph{upper Snell envelope $\ol{Z}$} of the reward process $Y$ is a supermartingale with respect to an appropriately defined nonlinear expectation $\ul{\sE}$, and $\ol{Z}$ is further an $\ul{\sE}-$martingale up to the first time $\t^*$ when $\ol{Z}$ meets $Y$. Consequently, $\t^*$ is the optimal stopping time for the robust optimal stopping problem and the corresponding zero-sum game has a value. Although the result seems similar to the one obtained in the classical optimal stopping theory, the mutual singularity of probabilities and the game aspect of the problem give rise to major technical hurdles, which we circumvent using some new methods.

Song Han, Junlong Kang, Huizi Mao et al.

Long Short-Term Memory (LSTM) is widely used in speech recognition. In order to achieve higher prediction accuracy, machine learning scientists have built larger and larger models. Such large model is both computation intensive and memory intensive. Deploying such bulky model results in high power consumption and leads to high total cost of ownership (TCO) of a data center. In order to speedup the prediction and make it energy efficient, we first propose a load-balance-aware pruning method that can compress the LSTM model size by 20x (10x from pruning and 2x from quantization) with negligible loss of the prediction accuracy. The pruned model is friendly for parallel processing. Next, we propose scheduler that encodes and partitions the compressed model to each PE for parallelism, and schedule the complicated LSTM data flow. Finally, we design the hardware architecture, named Efficient Speech Recognition Engine (ESE) that works directly on the compressed model. Implemented on Xilinx XCKU060 FPGA running at 200MHz, ESE has a performance of 282 GOPS working directly on the compressed LSTM network, corresponding to 2.52 TOPS on the uncompressed one, and processes a full LSTM for speech recognition with a power dissipation of 41 Watts. Evaluated on the LSTM for speech recognition benchmark, ESE is 43x and 3x faster than Core i7 5930k CPU and Pascal Titan X GPU implementations. It achieves 40x and 11.5x higher energy efficiency compared with the CPU and GPU respectively.