We study the problem of optimal continual fine-tuning for a pre-trained Foundation Model deployed at a resource-limited device. At each time slot, a new batch of training data arrives, and the controller is faced with two options: either use the data to fine-tune the model and incur a compute cost, or do not fine-tune the model and discard the data.

After the decision, the performance of the current model is measured in terms of an application-specific performance metric such as classification accuracy. Our objective is to learn an optimal policy that determines when to fine-tune the model on a single task (e.g., sentiment analysis), under a finite compute budget. We formulate this online decision-making problem as a constrained Markov Decision Process, where the system state captures three essential aspects: (i) model's performance, (ii) computational budget, and (iii) data distribution relevance to historic data encountered up to that point. The transition to the next state is stochastic and therefore, we propose a reinforcement learning-based method to solve this problem, namely the actor-critic algorithm. We also consider the special case where the performance of fine-tuning for a given model can be predicted or estimated prior to decision; in this case the problem becomes a Dynamic Programming one.

Experiments with a large pre-trained model on a widely-used text classification dataset demonstrate that our method consistently outperforms fine-tuning approaches with the same compute budget by more than $4\%$ in terms of accuracy and achieves $97\%$ of full-parameter fine-tuning accuracy while requiring only $25\%$ of the fine-tuning steps.