Improved Active Multi-Task Representation Learning via Lasso
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To leverage the copious amount of data from source tasks and overcome the scarcity of the target task samples, representation learning based on multi-task pretraining has become a standard approach in many applications. However, up until now, most existing works design a source task selection strategy from a purely empirical perspective. Recently, <cit.> gave the first active multi-task representation learning (A-MTRL) algorithm which adaptively samples from source tasks and can provably reduce the total sample complexity using the L2-regularized-target-source-relevance parameter ν^2. But their work is theoretically suboptimal in terms of total source sample complexity and is less practical in some real-world scenarios where sparse training source task selection is desired. In this paper, we address both issues. Specifically, we show the strict dominance of the L1-regularized-relevance-based (ν^1-based) strategy by giving a lower bound for the ν^2-based strategy. When ν^1 is unknown, we propose a practical algorithm that uses the LASSO program to estimate ν^1. Our algorithm successfully recovers the optimal result in the known case. In addition to our sample complexity results, we also characterize the potential of our ν^1-based strategy in sample-cost-sensitive settings. Finally, we provide experiments on real-world computer vision datasets to illustrate the effectiveness of our proposed method.
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