The field of online resource allocation and optimization is moving towards the development of more robust and flexible algorithms that can handle complex and uncertain environments. Researchers are exploring new approaches to incorporate exogenous replenishment, graphical dependencies, and smoothed analysis into online optimization problems. These innovations have the potential to significantly improve the performance and applicability of online algorithms in real-world settings. Notably, recent work has focused on designing tight competitive algorithms for online combinatorial optimization under Markov Random Fields and developing black-box methods for extending existing algorithms to handle arbitrary replenishment processes. Some particularly noteworthy papers include:

• A Black-Box Approach for Exogenous Replenishment in Online Resource Allocation, which introduces a black-box method for extending existing algorithms to handle arbitrary replenishment processes.
• Online Combinatorial Optimization with Graphical Dependencies, which presents general techniques for achieving tight competitive algorithms under Markov Random Fields.
• Smoothed Analysis of Online Metric Problems, which shows that polylogarithmic competitive ratios can be achieved for classical online problems under smoothed analysis.