Learning Conditional Invariances through Non-Commutativity
This work addresses domain adaptation challenges in machine learning by improving sample efficiency and target risk bounds, though it appears incremental as it builds on existing invariance learning frameworks.
The paper tackles the problem of learning conditional invariances in domain adaptation by relaxing invariance criteria to be non-commutatively directed towards the target domain, resulting in a method that surpasses state-of-the-art algorithms by over 2% in performance and approaches oracle-level accuracy.
Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder $\varphi^*$ that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder $Φ^*_τ$. We prove that non-commutativity steers the optimization towards $Φ^*_τ$ instead of $\varphi^*$, bringing the $\mathcal{H}$-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning $Φ^*_τ$, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over $2\%$, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.