While the ubiquitous adoption of algorithms in decision-making and content generation greatly improves societal efficiency, it has also raised various regulatory concerns, including antitrust, nondiscrimination, and intellectual property protection.

This dissertation investigates techniques from three different computer science research areas to support the regulation of algorithms: First, based on ideas from online learning theory, we propose a framework for the regulation of algorithmic collusion by auditing from data. Second, by adapting principles from information flow control with dynamic policies, we design a type system to reason about iteration (probabilistic) independence to support the regulation of the fairness of classification algorithms. Third, we study a proper data attribution notion informed by data privacy concepts for the regulation of credit attribution of generative models. These results demonstrate that the foundations of the regulation of algorithms can benefit from techniques from these distinct areas of computer science research and point to future research directions.