Optimal stopping problems with regime switching: a viscosity solution method

We employ the viscosity solution technique to analyze optimal stopping problems with regime switching. Specifically, we obtain the viscosity property of value functions, the uniqueness of viscosity solutions, the regularity of value functions and the form of optimal stopping intervals. Finally, we provide an application of the results.Comment: 29 pages, 1 figur

Semi-tied Units for Efficient Gating in LSTM and Highway Networks

Gating is a key technique used for integrating information from multiple sources by long short-term memory (LSTM) models and has recently also been applied to other models such as the highway network. Although gating is powerful, it is rather expensive in terms of both computation and storage as each gating unit uses a separate full weight matrix. This issue can be severe since several gates can be used together in e.g. an LSTM cell. This paper proposes a semi-tied unit (STU) approach to solve this efficiency issue, which uses one shared weight matrix to replace those in all the units in the same layer. The approach is termed "semi-tied" since extra parameters are used to separately scale each of the shared output values. These extra scaling factors are associated with the network activation functions and result in the use of parameterised sigmoid, hyperbolic tangent, and rectified linear unit functions. Speech recognition experiments using British English multi-genre broadcast data showed that using STUs can reduce the calculation and storage cost by a factor of three for highway networks and four for LSTMs, while giving similar word error rates to the original models.Comment: To appear in Proc. INTERSPEECH 2018, September 2-6, 2018, Hyderabad, Indi