Yannik Mahlau

Yannik Mahlau, Christian Nolde

In recent years, an abundance of feature attribution methods for explaining neural networks have been developed. Especially in the field of computer vision, many methods for generating saliency maps providing pixel attributions exist. However, their explanations often contradict each other and it is not clear which explanation to trust. A natural solution to this problem is the aggregation of multiple explanations. We present and compare different pixel-based aggregation schemes with the goal of generating a new explanation, whose fidelity to the model's decision is higher than each individual explanation. Using methods from the field of Bayesian Optimization, we incorporate the variance between the individual explanations into the aggregation process. Additionally, we analyze the effect of multiple normalization techniques on ensemble aggregation.

Yannik Mahlau, Frederik Schubert, Bodo Rosenhahn

The combination of self-play and planning has achieved great successes in sequential games, for instance in Chess and Go. However, adapting algorithms such as AlphaZero to simultaneous games poses a new challenge. In these games, missing information about concurrent actions of other agents is a limiting factor as they may select different Nash equilibria or do not play optimally at all. Thus, it is vital to model the behavior of the other agents when interacting with them in simultaneous games. To this end, we propose Albatross: AlphaZero for Learning Bounded-rational Agents and Temperature-based Response Optimization using Simulated Self-play. Albatross learns to play the novel equilibrium concept of a Smooth Best Response Logit Equilibrium (SBRLE), which enables cooperation and competition with agents of any playing strength. We perform an extensive evaluation of Albatross on a set of cooperative and competitive simultaneous perfect-information games. In contrast to AlphaZero, Albatross is able to exploit weak agents in the competitive game of Battlesnake. Additionally, it yields an improvement of 37.6% compared to previous state of the art in the cooperative Overcooked benchmark.

Yannik Mahlau, Yannick Augenstein, Tyler W. Hughes et al.

Inverse design, particularly geometric shape optimization, provides a systematic approach for developing high-performance nanophotonic devices. While numerous optimization algorithms exist, previous global approaches exhibit slow convergence and conversely local search strategies frequently become trapped in local optima. To address the limitations inherent to both local and global approaches, we introduce BONNI: Bayesian optimization through neural network ensemble surrogates with interior point optimization. It augments global optimization with an efficient incorporation of gradient information to determine optimal sampling points. This capability allows BONNI to circumvent the local optima found in many nanophotonic applications, while capitalizing on the efficiency of gradient-based optimization. We demonstrate BONNI's capabilities in the design of a distributed Bragg reflector as well as a dual-layer grating coupler through an exhaustive comparison against other optimization algorithms commonly used in literature. Using BONNI, we were able to design a 10-layer distributed Bragg reflector with only 4.5% mean spectral error, compared to the previously reported results of 7.8% error with 16 layers. Further designs of a broadband waveguide taper and photonic crystal waveguide transition validate the capabilities of BONNI.

Yannik Mahlau, Maximilian Schier, Christoph Reinders et al.

Inverse design of photonic integrated circuits (PICs) has traditionally relied on gradientbased optimization. However, this approach is prone to end up in local minima, which results in suboptimal design functionality. As interest in PICs increases due to their potential for addressing modern hardware demands through optical computing, more adaptive optimization algorithms are needed. We present a reinforcement learning (RL) environment as well as multi-agent RL algorithms for the design of PICs. By discretizing the design space into a grid, we formulate the design task as an optimization problem with thousands of binary variables. We consider multiple two- and three-dimensional design tasks that represent PIC components for an optical computing system. By decomposing the design space into thousands of individual agents, our algorithms are able to optimize designs with only a few thousand environment samples. They outperform previous state-of-the-art gradient-based optimization in both twoand three-dimensional design tasks. Our work may also serve as a benchmark for further exploration of sample-efficient RL for inverse design in photonics.