Unrolling SGD: Understanding Factors Influencing Machine Unlearning

Abstract

Machine unlearning is the process through which a deployed machine learning model forgets about one of its training data points. While naively retraining the model from scratch is an option, it is almost always associated with a large computational effort for deep learning models. Thus, several approaches to approximately unlearn have been proposed along with corresponding metrics that formalize what it means for a model to forget about a data point. In this work, we first taxonomize approaches and metrics of approximate unlearning. As a result, we identify verification error, i.e., the 2 difference between the weights of an approximately unlearned and a naively retrained model, as a metric approximate unlearning should optimize for as it implies a large class of other metrics. We theoretically analyze the canonical stochastic gradient descent (SGD) training algorithm to surface the variables which are relevant to reducing the verification error of approximate unlearning for SGD. From this analysis, we first derive an easy-to-compute proxy for verification error (termed unlearning error). The analysis also informs the design of a new training objective penalty that limits the overall change in weights during SGD and as a result facilitates approximate unlearning with lower verification error. We validate our theoretical work through an empirical evaluation on CIFAR-10, CIFAR-100, and IMDB sentiment analysis.

Towards Adversarial Evaluations for Inexact Machine Unlearning

“…Scalability to large deletion sets: Many prior unlearning methods assume tiny deletion sets [11,30,53,61,68]. However, we argue practical applications typically require the deletion of larger subsets of data, necessitating that unlearning procedures should scale well to this setting.…”

“…Second, the prohibitive cost of collecting a representative sample of deep networks makes it infeasible to measure the equivalence of model distributions. Most prior work addresses this by measuring similarity of weights [39,61,68] or outputs [27][28][29]51] between a single model sampled from φ u and φ r . However, measuring similarity between two model instances is not representative of the similarity between the distributions they are drawn from.…”

On the Necessity of Auditable Algorithmic Definitions for Machine Unlearning

“…Since then further extensions to scenarios where efficient analytic solutions could be found were given [24,9], and an extension to unlearn deep neural networks (DNNs) were proposed [2,13,20,12,11,10]. With the growing field of unlearning, there has emerged two categories of machine unlearning algorithms [23]: exact and approximate unlearning, differing by how unlearning is done, and also how the concept of "unlearning" is understood. Exact unlearning for DNNs is based on retraining.…”

“…Existing work have proposed to use techniques such as membership inference [21] to verify the effectiveness of approximate unlearning [12,1] to show that their approximately unlearned models cannot be easily distinguished from models that are not trained on the data points to be unlearned. Alternatively, others compare the similarity of the approximately unlearned models parameters to exactly unlearned models parameters [10,11,25,23].…”

“…In previous literature related to unlearning [23,12,10,11], a model is said to have unlearned if the impact of the data points to be unlearned is removed from the model, where removing the impact of the data points from the model is equivalent to obtaining a model that one could get from retraining without those points. In other words, a model is unlearned if its parameters are in the subspace of the parameter space that can be achieved by training on a dataset that does not contain the points to be unlearned; further work requires the process of obtaining those parameters to also reproduce the same distribution one gets from retraining [10,11,13].…”