# Mathematical Finance & Financial Data Science Seminar

#### Improving Reinforcement Learning Algorithms: Towards Optimal Learning Rate Policies

**Speaker:**
Charles-Albert Lehalle, Capital Fund Management (CFM)

**Location:**
Warren Weaver Hall (Email organizer for room location)

**Date:**
Wednesday, November 13, 2019, 4 p.m.

**Synopsis:**

This paper investigates to what extent we can improve stochastic algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate $O(1/\sqrt{N})$ is pessimistic and can be replaced by $O((\log(N)/N)^{\beta})$ with $\frac{1}{2}\leq \beta \leq 1$ and $N$ the number of iterations. Second, we propose a dynamic optimal policy for the choice of the learning rate $(\gamma_k)_{k\geq 0}$ used in stochastic algorithms. We decompose our policy into two interacting levels: the inner and the outer level. In the inner level, we present the PASS algorithm (for ``PAst Sign Search'') which, based on a predefined sequence $(\gamma^o_k)_{k\geq 0}$, constructs a new sequence $(\gamma^i_k)_{k\geq 0}$ that converges faster. In the outer level, we propose an optimal methodology for the selection of the predefined sequence $(\gamma^o_k)_{k\geq 0}$. Third, we show empirically that our selection methodology of the learning rate outperforms significantly standard algorithms used in reinforcement learning (RL) in the three following applications: the estimation of a drift, the optimal placement of limit orders and the optimal execution of large number of shares. The two last applications are useful for financial markets.

**Notes:**

This seminar is part of the Quant Finance & Financial Data Science Working Group's activities at NYU Courant. As space is limited to this seminar, if you would like to attend please email Petter Kolm (petter DOT kolm AT nyu DOT edu) for the room assignment.