We first prove the direction Z T SI (Z; T) = 0, which is equivalent to prove I ( Z; T) = 0 SI (Z; T) = 0 . We now consider the direction SI (Z; T) = 0 Z T . Now consider the moment generating functions. T)) > 0 for the chosen h, g, θ, ϕ (since h, g are not constant functions). A.2 Proof of Theorem 2 Theorem 2. Provided that each h We prove the contrapositive, i.e. rather than show LHS = RHS, we show that RHS = LHS .

The task of infomin learning aims to learn a representation with high utility while being uninformative about a specified target, with the latter achieved by minimis-ing the mutual information between the representation and the target. It has broad applications, ranging from training fair prediction models against protected attributes, to unsupervised learning with disentangled representations. Recent works on infomin learning mainly use adversarial training, which involves training a neural network to estimate mutual information or its proxy and thus is slow and difficult to optimise. Drawing on recent advances in slicing techniques, we propose a new infomin learning approach, which uses a novel proxy metric to mutual information. We further derive an accurate and analytically computable approximation to this proxy metric, thereby removing the need of constructing neural network-based mutual information estimators. Experiments on algorithmic fairness, disentangled representation learning and domain adaptation verify that our method can effectively remove unwanted information with limited time budget.

Deep Reinforcement Learning (Deep-RL) techniques for motion control have been continuously used to deal with decision-making problems for a wide variety of robots. Previous works showed that Deep-RL can be applied to perform mapless navigation, including the medium transition of Hybrid Unmanned Aerial Underwater Vehicles (HUAUVs). These are robots that can operate in both air and water media, with future potential for rescue tasks in robotics. This paper presents new approaches based on the state-of-the-art Double Critic Actor-Critic algorithms to address the navigation and medium transition problems for a HUAUV. We show that double-critic Deep-RL with Recurrent Neural Networks using range data and relative localization solely improves the navigation performance of HUAUVs. Our DoCRL approaches achieved better navigation and transitioning capability, outperforming previous approaches.

The task of infomin learning aims to learn a representation with high utility while being uninformative about a specified target, with the latter achieved by minimising the mutual information between the representation and the target. It has broad applications, ranging from training fair prediction models against protected attributes, to unsupervised learning with disentangled representations. Recent works on infomin learning mainly use adversarial training, which involves training a neural network to estimate mutual information or its proxy and thus is slow and difficult to optimise. Drawing on recent advances in slicing techniques, we propose a new infomin learning approach, which uses a novel proxy metric to mutual information. We further derive an accurate and analytically computable approximation to this proxy metric, thereby removing the need of constructing neural network-based mutual information estimators. Experiments on algorithmic fairness, disentangled representation learning and domain adaptation verify that our method can effectively remove unwanted information with limited time budget.

Minimax optimization plays a key role in adversarial training of machine learning algorithms, such as learning generative models, domain adaptation, privacy preservation, and robust learning. In this paper, we demonstrate the failure of alternating gradient descent in minimax optimization problems due to the discontinuity of solutions of the inner maximization. To address this, we propose a new epsilon-subgradient descent algorithm that addresses this problem by simultaneously tracking K candidate solutions. Practically, the algorithm can find solutions that previous saddle-point algorithms cannot find, with only a sublinear increase of complexity in K. We analyze the conditions under which the algorithm converges to the true solution in detail. A significant improvement in stability and convergence speed of the algorithm is observed in simple representative problems, GAN training, and domain-adaptation problems.