We consider online model selection with decentralized data over M clients, and study the necessity of collaboration among clients. Previous work proposed various federated algorithms without demonstrating their necessity, while we answer the question from a novel perspective of computational constraints. We prove lower bounds on the regret, and propose a federated algorithm and analyze the upper bound. Our results show (i) collaboration is unnecessary in the absence of computational constraints on clients; (ii) collaboration is necessary if the computational cost on each client is limited to o(K), where K is the number of candidate hypothesis spaces. We clarify the unnecessary nature of collaboration in previous federated algorithms for distributed online multi-kernel learning, and improve the regret bounds at a smaller computational and communication cost.

Recent works for time-series forecasting more and more leverage the high predictive power of Deep Learning models. With this increase in model complexity, however, comes a lack in understanding of the underlying model decision process, which is problematic for high-stakes decision making. At the same time, simple, interpretable forecasting methods such as Linear Models can still perform very well, sometimes on-par, with Deep Learning approaches. We argue that simple models are good enough most of the time, and forecasting performance can be improved by choosing a Deep Learning method only for certain predictions, increasing the overall interpretability of the forecasting process. In this context, we propose a novel online model selection framework which uses meta-learning to identify these predictions and only rarely uses a non-interpretable, large model. An extensive empirical study on various real-world datasets shows that our selection methodology outperforms state-of-the-art online model selections methods in most cases. We find that almost always choosing a simple Linear Model for forecasting results in competitive performance, suggesting that the need for opaque black-box models in time-series forecasting is smaller than recent works would suggest.

Web-based applications such as chatbots, search engines and news recommendations continue to grow in scale and complexity with the recent surge in the adoption of LLMs. Online model selection has thus garnered increasing attention due to the need to choose the best model among a diverse set while balancing task reward and exploration cost. Organizations faces decisions like whether to employ a costly API-based LLM or a locally finetuned small LLM, weighing cost against performance. Traditional selection methods often evaluate every candidate model before choosing one, which are becoming impractical given the rising costs of training and finetuning LLMs. Moreover, it is undesirable to allocate excessive resources towards exploring poor-performing models. While some recent works leverage online bandit algorithm to manage such exploration-exploitation trade-off in model selection, they tend to overlook the increasing-then-converging trend in model performances as the model is iteratively finetuned, leading to less accurate predictions and suboptimal model selections. In this paper, we propose a time-increasing bandit algorithm TI-UCB, which effectively predicts the increase of model performances due to finetuning and efficiently balances exploration and exploitation in model selection. To further capture the converging points of models, we develop a change detection mechanism by comparing consecutive increase predictions. We theoretically prove that our algorithm achieves a logarithmic regret upper bound in a typical increasing bandit setting, which implies a fast convergence rate. The advantage of our method is also empirically validated through extensive experiments on classification model selection and online selection of LLMs. Our results highlight the importance of utilizing increasing-then-converging pattern for more efficient and economic model selection in the deployment of LLMs.

Online model selection involves selecting a model from a set of candidate models 'on the fly' to perform prediction on a stream of data. The choice of candidate models henceforth has a crucial impact on the performance. Although employing a larger set of candidate models naturally leads to more flexibility in model selection, this may be infeasible in cases where prediction tasks are performed on edge devices with limited memory. Faced with this challenge, the present paper proposes an online federated model selection framework where a group of learners (clients) interacts with a server with sufficient memory such that the server stores all candidate models. However, each client only chooses to store a subset of models that can be fit into its memory and performs its own prediction task using one of the stored models. Furthermore, employing the proposed algorithm, clients and the server collaborate to fine-tune models to adapt them to a non-stationary environment. Theoretical analysis proves that the proposed algorithm enjoys sub-linear regret with respect to the best model in hindsight. Experiments on real datasets demonstrate the effectiveness of the proposed algorithm.

Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and early theoretical results on linear Markov decision processes provide regret bounds that scale with the dimension of the linear approximation. Ideally, we would like to automatically identify the minimal dimension of the approximation that is sufficient to encode an optimal policy. Towards this end, we consider the problem of model selection in RL with function approximation, given a set of candidate RL algorithms with known regret guarantees. The learner's goal is to adapt to the complexity of the optimal algorithm without knowing it \textit{a priori}. We present a meta-algorithm that successively rejects increasingly complex models using a simple statistical test. Given at least one candidate that satisfies realizability, we prove the meta-algorithm adapts to the optimal complexity with $\tilde{O}(L^{5/6} T^{2/3})$ regret compared to the optimal candidate's $\tilde{O}(\sqrt T)$ regret, where $T$ is the number of episodes and $L$ is the number of algorithms. The dimension and horizon dependencies remain optimal with respect to the best candidate, and our meta-algorithmic approach is flexible to incorporate multiple candidate algorithms and models. Finally, we show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds that depend on the gaps between the maximal values attainable by the candidates.

Both the human brain and artificial learning agents operating in real-world or comparably complex environments are faced with the challenge of online model selection. In principle this challenge can be overcome: hierarchical Bayesian inference provides a principled method for model selection and it converges on the same posterior for both off-line (i.e. batch) and online learning. However, maintaining a parameter posterior for each model in parallel has in general an even higher memory cost than storing the entire data set and is consequently clearly unfeasible. Alternatively, maintaining only a limited set of models in memory could limit memory requirements. However, sufficient statistics for one model will usually be insufficient for fitting a different kind of model, meaning that the agent loses information with each model change. We propose that episodic memory can circumvent the challenge of limited memory-capacity online model selection by retaining a selected subset of data points. We design a method to compute the quantities necessary for model selection even when the data is discarded and only statistics of one (or few) learnt models are available. We demonstrate on a simple model that a limited-sized episodic memory buffer, when the content is optimised to retain data with statistics not matching the current representation, can resolve the fundamental challenge of online model selection.