Research Group "Stochastic Algorithms and Nonparametric Statistics"

Seminar "Modern Methods in Applied Stochastics and Nonparametric Statistics" Winter Semester 2022/23


11.10.2022 Thomas Wagenhofer (TU Berlin)
Weak error estimates for rough volatility models
We consider a rough volatility model where the volatility is a (smooth) function of a Riemann--Liouville Brownian motion with Hurst parameter H in (0,1/2). When simulating these models, one often uses a discretization of stochastic integrals as an approximation. These integrals can be interpreted as log-stock-prices. In Applications, such as in pricing, the most relevent quantities are expectations of (payoff) functions. Our main result is that moments of these integrals have a weak error rate of order 3H+1/2 if H<1/6 and order 1 otherwise. For this we first derive a moment formula for both the discretization and the true stochastic integral. We then use this formula and properties of Gaussian random variables to prove our main theorems. We furthermore show that this convergence rate also holds for slightly more general payoffs and also provide a lower bound. Note that our rate of 3H+1/2 is in stark contrast to the strong error rate which is of order H. This is a joint work with Peter Friz and William Salkeld.
18.10.2022 Egor Gladin (Humboldt Universität zu Berlin)
Algorithm for constrained Markov decision process with linear convergence (hybrid talk)
The problem of constrained Markov decision process is considered. An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs (the number of constraints is relatively small). A new dual approach is proposed with the integration of two ingredients: entropy-regularized policy optimizer and Vaidya's dual optimizer, both of which are critical to achieve faster convergence. The finite-time error bound of the proposed approach is provided. Despite the challenge of the nonconcave objective subject to nonconcave constraints, the proposed approach is shown to converge (with linear rate) to the global optimum. The complexity expressed in terms of the optimality gap and the constraint violation significantly improves upon the existing primal-dual approaches.
25.10.2022 Luca Pelizzari (WIAS Berlin)
Polynomial Volterra processes and rough polynomial models (hybrid talk)
01.11.2022 Alexandra Suvorikova (WIAS Berlin)
Robust k-means clustering (hybrid talk)
In this work we investigate the theoretical properties of robust k-means clustering under assumption of adversarial data corruption. We provide non-asymptotic rates for excess distortion under weak model assumptions on the moments of the distribution.

ESH, Mohrenstr. 39
22.11.2022 Dr. Pavel Dvurechensky (WIAS Berlin)
Generalized self-concordant analysis of Frank-Wolfe algorithms (hybrid talk)
We propose several variants of the Frank-Wolfe method for minimizing generalized self-concordant (GSC) functions over compact sets. Such problems are ill-conditioned and are motivated by machine learning applications such as inverse covariance estimation or distance-weighted discrimination problems in support vector machines. We obtain O(1/k) convergence rate guarantees in the general situation and linear convergence under strong convexity and additional assumptions.

06.12.2022 Robert Gruhlke (WIAS Berlin)

13.12.2022 Dr. Amal Alphonse (WIAS Berlin)
Risk-averse optimal control of random elliptic variational inequalities (hybrid talk)
In this talk, I will discuss a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. I will derive two forms of first-order stationarity conditions for the problem by passing to the limit in a penalised and smoothed approximating control problem. The lack of regularity with respect to the uncertain parameters and complexities induced by the presence of the risk measure give rise to delicate analytical challenges seemingly unique to the stochastic setting. To finish, I will briefly discuss a path-following stochastic approximation algorithm and demonstrate it on an example.

last reviewed: November 22, 2022 by Christine Schneider