Hyperparameter tuning of deep learning models can lead to order-of-magnitude performance gains for the same amount of compute. Despite this, systematic tuning is uncommon, particularly for large models, which are expensive to evaluate and tend to have many hyperparameters, necessitating difficult judgment calls about tradeoffs, budgets, and search bounds. To address these issues and propose a practical method for robustly tuning large models, we present Cost-Aware Pareto Region Bayesian Search (CARBS), a Bayesian optimization algorithm that performs local search around the performance-cost Pareto frontier. CARBS does well even in unbounded search spaces with many hyperparameters, learns scaling relationships so that it can tune models even as they are scaled up, and automates much of the "black magic" of tuning. Among our results, we effectively solve the entire ProcGen benchmark just by tuning a simple baseline (PPO, as provided in the original ProcGen paper). We also reproduce the model size vs. training tokens scaling result from the Chinchilla project (Hoffmann et al. 2022), while simultaneously discovering scaling laws for every other hyperparameter, via an easy automated process that uses significantly less compute and is applicable to any deep learning problem (not just language models).

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this conclusion via the study of a linearized model of Barlow Twins applicable to the case in which the trained network is infinitely wide. We solve the training dynamics of this model from small initialization, finding that the model learns the top eigenmodes of a certain contrastive kernel in a stepwise fashion, and obtain a closed-form expression for the final learned representations. Remarkably, we then see the same stepwise learning phenomenon when training deep ResNets using the Barlow Twins, SimCLR, and VICReg losses. Our theory suggests that, just as kernel regression can be thought of as a model of supervised learning, kernel PCA may serve as a useful model of self-supervised learning.

Adaptive traffic signal control is one key avenue for mitigating the growing consequences of traffic congestion. Incumbent solutions such as SCOOT and SCATS require regular and time-consuming calibration, can't optimise well for multiple road use modalities, and require the manual curation of many implementation plans. A recent alternative to these approaches are deep reinforcement learning algorithms, in which an agent learns how to take the most appropriate action for a given state of the system. This is guided by neural networks approximating a reward function that provides feedback to the agent regarding the performance of the actions taken, making it sensitive to the specific reward function chosen. Several authors have surveyed the reward functions used in the literature, but attributing outcome differences to reward function choice across works is problematic as there are many uncontrolled differences, as well as different outcome metrics. This paper compares the performance of agents using different reward functions in a simulation of a junction in Greater Manchester, UK, across various demand profiles, subject to real world constraints: realistic sensor inputs, controllers, calibrated demand, intergreen times and stage sequencing. The reward metrics considered are based on the time spent stopped, lost time, change in lost time, average speed, queue length, junction throughput and variations of these magnitudes. The performance of these reward functions is compared in terms of total waiting time. We find that speed maximisation resulted in the lowest average waiting times across all demand levels, displaying significantly better performance than other rewards previously introduced in the literature.