Improved Active Multi-Task Representation Learning via Lasso
Yiping Wang Yifang Chen Kevin Jamieson Simon S. Du
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, \citet{chen2022active}
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
$\nu^2$. 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 ($\nu^1$-based) strategy by giving a lower bound
for the $\nu^2$-based strategy. When $\nu^1$ is unknown, we propose a practical
algorithm that uses the LASSO program to estimate $\nu^1$. 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
$\nu^1$-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.