Improving Thompson Sampling via Information Relaxation for Budgeted Multi-armed Bandits

We consider a Bayesian budgeted multi-armed bandit problem, in which each arm consumes a different amount of resources when selected and there is a budget constraint on the total amount of resources that can be used. Budgeted Thompson Sampling (BTS) offers a very effective heuristic to this problem, but its arm-selection rule does not take into account the remaining budget information. We adopt \textit{Information Relaxation Sampling} framework that generalizes Thompson Sampling for classical $K$-armed bandit problems, and propose a series of algorithms that are randomized like BTS but more carefully optimize their decisions with respect to the budget constraint. In a one-to-one correspondence with these algorithms, a series of performance benchmarks that improve the conventional benchmark are also suggested. Our theoretical analysis and simulation results show that our algorithms (and our benchmarks) make incremental improvements over BTS (respectively, the conventional benchmark) across various settings including a real-world example.

Leveraging Priors via Diffusion Bridge for Time Series Generation

Time series generation is widely used in real-world applications such as simulation, data augmentation, and hypothesis test techniques. Recently, diffusion models have emerged as the de facto approach for time series generation, emphasizing diverse synthesis scenarios based on historical or correlated time series data streams. Since time series have unique characteristics, such as fixed time order and data scaling, standard Gaussian prior might be ill-suited for general time series generation. In this paper, we exploit the usage of diverse prior distributions for synthesis. Then, we propose TimeBridge, a framework that enables flexible synthesis by leveraging diffusion bridges to learn the transport between chosen prior and data distributions. Our model covers a wide range of scenarios in time series diffusion models, which leverages (i) data- and time-dependent priors for unconditional synthesis, and (ii) data-scale preserving synthesis with a constraint as a prior for conditional generation. Experimentally, our model achieves state-of-the-art performance in both unconditional and conditional time series generation tasks.