Jack Geary

Jack Geary, Boyan Gao, Henry Gouk

We consider the problem of strategic classification, where the act of deploying a classifier leads to strategic behaviour that induces a distribution shift on subsequent observations. Current approaches to learning classifiers in strategic settings are focused primarily on the linear setting, but in many cases non-linear classifiers are more suitable. A central limitation to progress for non-linear classifiers arises from the inability to compute best responses in these settings. We present a novel method for computing the best response by optimising the Lagrangian dual of the Agents' objective. We demonstrate that our method reproduces best responses in linear settings, identifying key weaknesses in existing approaches. We present further results demonstrating our method can be straight-forwardly applied to non-linear classifier settings, where it is useful for both evaluation and training.

Jack Geary, Boyan Gao, Henry Gouk

Algorithmic developments in Strategic Classification have been mostly limited to linear classifiers in settings where the best response has a closed-form solution or can be easily approximated. While some work has explored the role of non-linear classifiers in strategic settings, progress in this direction is impeded by the computational intractability of the strategic behaviour. Addressing this, we present a novel method for approximating the best response by exploiting Lagrangian duality. By reformulating the strategic response as a constrained optimisation problem, we can construct a Lagrangian that is amenable to first order optimisation methods. This approach reproduces closed-form strategic behaviour in linear settings and can be straight-forwardly applied to non-linear settings. We show how the Implicit Function Theorem can be used in conjunction with our proposed response formulation during classifier learning to compute the total gradient of the loss. This connects the classifier parameters directly to the consequent strategic behaviour, yielding a novel training algorithm that can exploit this relationship. Experimental evaluation shows that the resulting models achieve improved strategic accuracy on common machine learning datasets.

Jack Geary, Henry Gouk

We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is restricted to deterministic classifiers. In contrast, we perform a theoretical analysis of an extension to this setting that allows the learner to produce a randomised classifier. We show that, under certain conditions, the optimal randomised classifier can achieve better accuracy than the optimal deterministic classifier, but under no conditions can it be worse. When a finite set of training data is available, we show that the excess risk of Strategic Empirical Risk Minimisation over the class of randomised classifiers is bounded in a similar manner as the deterministic case. In both the deterministic and randomised cases, the risk of the classifier produced by the learner converges to that of the corresponding optimal classifier as the volume of available training data grows. Moreover, this convergence happens at the same rate as in the i.i.d. case. Our findings are compared with previous theoretical work analysing the problem of strategic classification. We conclude that randomisation has the potential to alleviate some issues that could be faced in practice without introducing any substantial downsides.

Jack Geary, Henry Gouk, Subramanian Ramamoorthy

Safe interaction between vehicles requires the ability to choose actions that reveal the preferences of the other vehicles. Since exploratory actions often do not directly contribute to their objective, an interactive vehicle must also able to identify when it is appropriate to perform them. In this work we demonstrate how Active Learning methods can be used to incentivise an autonomous vehicle (AV) to choose actions that reveal information about the altruistic inclinations of another vehicle. We identify a property, Information Sufficiency, that a reward function should have in order to keep exploration from unnecessarily interfering with the pursuit of an objective. We empirically demonstrate that reward functions that do not have Information Sufficiency are prone to inadequate exploration, which can result in sub-optimal behaviour. We propose a reward definition that has Information Sufficiency, and show that it facilitates an AV choosing exploratory actions to estimate altruistic tendency, whilst also compensating for the possibility of conflicting beliefs between vehicles.