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Explore the foundations of competitive analysis in online algorithms through this comprehensive lecture from the Simons Institute's Data-Driven Decision Processes Boot Camp. Delve into the vibrant research area of online algorithms, focusing on decision-making under uncertainty. Learn about the competitive analysis framework, which compares the performance of online algorithms making decisions without future knowledge to the best dynamic sequence of decisions in hindsight. Discover the model definition, representative problems, solution techniques, and proof strategies employed in competitive analysis. Gain insights from Anupam Gupta of Carnegie Mellon University as he introduces this crucial aspect of computer science research, setting the stage for a deeper understanding of online decision-making processes.