Online Regenerative Learning
This addresses efficiency challenges in online optimization for real-world scenarios where inputs may not be i.i.d., but it is incremental as it builds on existing OLP frameworks.
The paper tackles the problem of Online Linear Programming with non-i.i.d. stochastic inputs, showing that for stationary regenerative inputs, popular algorithms achieve regret bounds similar to i.i.d. cases, and proposing a trend-adaptive algorithm for trendy, non-stationary inputs.
We study a type of Online Linear Programming (OLP) problem that maximizes the objective function with stochastic inputs. The performance of various algorithms that analyze this type of OLP is well studied when the stochastic inputs follow some i.i.d distribution. The two central questions to ask are: (i) can the algorithms achieve the same efficiency if the stochastic inputs are not i.i.d but still stationary, and (ii) how can we modify our algorithms if we know the stochastic inputs are trendy, hence not stationary. We answer the first question by analyzing a regenerative type of input and show the regrets of two popular algorithms are bounded by the same orders as their i.i.d counterparts. We discuss the second question in the context of linearly growing inputs and propose a trend-adaptive algorithm. We provide numerical simulations to illustrate the performance of our algorithms under both regenerative and trendy inputs.