Mojmir Mutny

Melis Ilayda Bal, Pier Giuseppe Sessa, Mojmir Mutny et al.

Bayesian optimization (BO) is a powerful framework to optimize black-box expensive-to-evaluate functions via sequential interactions. In several important problems (e.g. drug discovery, circuit design, neural architecture search, etc.), though, such functions are defined over large $\textit{combinatorial and unstructured}$ spaces. This makes existing BO algorithms not feasible due to the intractable maximization of the acquisition function over these domains. To address this issue, we propose $\textbf{GameOpt}$, a novel game-theoretical approach to combinatorial BO. $\textbf{GameOpt}$ establishes a cooperative game between the different optimization variables, and selects points that are game $\textit{equilibria}$ of an upper confidence bound acquisition function. These are stable configurations from which no variable has an incentive to deviate$-$ analog to local optima in continuous domains. Crucially, this allows us to efficiently break down the complexity of the combinatorial domain into individual decision sets, making $\textbf{GameOpt}$ scalable to large combinatorial spaces. We demonstrate the application of $\textbf{GameOpt}$ to the challenging $\textit{protein design}$ problem and validate its performance on four real-world protein datasets. Each protein can take up to $20^{X}$ possible configurations, where $X$ is the length of a protein, making standard BO methods infeasible. Instead, our approach iteratively selects informative protein configurations and very quickly discovers highly active protein variants compared to other baselines.

Mojmir Mutny

A stochastic iterative algorithm approximating second-order information using von Neumann series is discussed. We present convergence guarantees for strongly-convex and smooth functions. Our analysis is much simpler in contrast to a similar algorithm and its analysis, LISSA. The algorithm is primarily suitable for training large scale linear models, where the number of data points is very large. Two novel analyses, one showing space independent linear convergence, and one showing conditional quadratic convergence are discussed. In numerical experiments, the behavior of the error is similar to the second-order algorithm L-BFGS, and improves the performance of LISSA for quadratic objective function.

Johannes Kirschner, Andreas Krause, Michele Meziu et al.

We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and establish fundamental connections between sequential mixing, Bayesian inference and regret inequalities from online estimation. The framework applies to any realizable family of likelihood functions and allows for non-i.i.d. data and anytime validity. Moreover, the framework seamlessly integrates standard approximate inference techniques, such as variational inference and sampling-based methods, and extends to misspecified model classes, while preserving provable coverage guarantees. We illustrate the power of the framework by deriving tighter confidence sequences for classical settings, including sequential linear regression and sparse estimation, with simplified proofs.

Lenart Treven, Sebastian Curi, Mojmir Mutny et al.

The principal task to control dynamical systems is to ensure their stability. When the system is unknown, robust approaches are promising since they aim to stabilize a large set of plausible systems simultaneously. We study linear controllers under quadratic costs model also known as linear quadratic regulators (LQR). We present two different semi-definite programs (SDP) which results in a controller that stabilizes all systems within an ellipsoid uncertainty set. We further show that the feasibility conditions of the proposed SDPs are \emph{equivalent}. Using the derived robust controller syntheses, we propose an efficient data dependent algorithm -- \textsc{eXploration} -- that with high probability quickly identifies a stabilizing controller. Our approach can be used to initialize existing algorithms that require a stabilizing controller as an input while adding constant to the regret. We further propose different heuristics which empirically reduce the number of steps taken by \textsc{eXploration} and reduce the suffered cost while searching for a stabilizing controller.

Mojmir Mutny, Rahul Nair, Jens-Malte Gottfried

The Multipath effect in Time-of-Flight(ToF) cameras still remains to be a challenging problem that hinders further processing of 3D data information. Based on the evidence from previous literature, we explored the possibility of using machine learning techniques to correct this effect. Firstly, we created two new datasets of of ToF images rendered via ToF simulator of LuxRender. These two datasets contain corners in multiple orientations and with different material properties. We chose scenes with corners as multipath effects are most pronounced in corners. Secondly, we used this dataset to construct a learning model to predict real valued corrections to the ToF data using Random Forests. We found out that in our smaller dataset we were able to predict real valued correction and improve the quality of depth images significantly by removing multipath bias. With our algorithm, we improved relative per-pixel error from average value of 19% to 3%. Additionally, variance of the error was lowered by an order of magnitude.