Path Integral Optimiser: Global Optimisation via Neural Schrödinger-Föllmer Diffusion

We present an early investigation into the use of neural diffusion processes for global optimisation, focusing on Zhang et al.'s Path Integral Sampler. One can use the Boltzmann distribution to formulate optimization as solving a Schr\"odinger bridge sampling problem, then apply Girsanov's theorem with a simple (single-point) prior to frame it in stochastic control terms, and compute the solution's integral terms via a neural approximation (a Fourier MLP). We provide theoretical bounds for this optimiser, results on toy optimisation tasks, and a summary of the stochastic theory motivating the model. Ultimately, we found the optimiser to display promising per-step performance at optimisation tasks between 2 and 1,247 dimensions, but struggle to explore higher-dimensional spaces when faced with a 15.9k parameter model, indicating a need for work on adaptation in such environments.

Skill Issues: An Analysis of CS:GO Skill Rating Systems

The meteoric rise of online games has created a need for accurate skill rating systems for tracking improvement and fair matchmaking. Although many skill rating systems are deployed, with various theoretical foundations, less work has been done at analysing the real-world performance of these algorithms. In this paper, we perform an empirical analysis of Elo, Glicko2 and TrueSkill through the lens of surrogate modelling, where skill ratings influence future matchmaking with a configurable acquisition function. We look both at overall performance and data efficiency, and perform a sensitivity analysis based on a large dataset of Counter-Strike: Global Offensive matches.

Learning-Rate-Free Learning: Dissecting D-Adaptation and Probabilistic Line Search

This paper explores two recent methods for learning rate optimisation in stochastic gradient descent: D-Adaptation (arXiv:2301.07733) and probabilistic line search (arXiv:1502.02846). These approaches aim to alleviate the burden of selecting an initial learning rate by incorporating distance metrics and Gaussian process posterior estimates, respectively. In this report, I provide an intuitive overview of both methods, discuss their shared design goals, and devise scope for merging the two algorithms.