A representation-learning game for classes of prediction tasks
This work addresses representation learning for scenarios with uncertain future tasks, which is incremental as it builds on existing game-theoretic and representation learning frameworks.
The paper tackles the problem of learning dimensionality-reducing representations when only prior knowledge about future prediction tasks is available, using a game-based formulation where one player chooses a representation and another adversarially selects a task to maximize regret. It derives theoretically optimal representations for linear settings and proposes an efficient algorithm for general cases, showing the effectiveness of prior knowledge and the utility of randomization.
We propose a game-based formulation for learning dimensionality-reducing representations of feature vectors, when only a prior knowledge on future prediction tasks is available. In this game, the first player chooses a representation, and then the second player adversarially chooses a prediction task from a given class, representing the prior knowledge. The first player aims is to minimize, and the second player to maximize, the regret: The minimal prediction loss using the representation, compared to the same loss using the original features. For the canonical setting in which the representation, the response to predict and the predictors are all linear functions, and under the mean squared error loss function, we derive the theoretically optimal representation in pure strategies, which shows the effectiveness of the prior knowledge, and the optimal regret in mixed strategies, which shows the usefulness of randomizing the representation. For general representations and loss functions, we propose an efficient algorithm to optimize a randomized representation. The algorithm only requires the gradients of the loss function, and is based on incrementally adding a representation rule to a mixture of such rules.