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1. Quantifying the Benefit of Using Differentiable Learning over Tangent Kernels

   Malach, Eran; Kamath, Pritish; Abbe, Emmanuel; Srebro, Nathan (July 2021, Proceedings of Machine Learning Research)

   null (Ed.)

   We study the relative power of learning with gradient descent on differentiable models, such as neural networks, versus using the corresponding tangent kernels. We show that under certain conditions, gradient descent achieves small error only if a related tangent kernel method achieves a non-trivial advantage over random guessing (a.k.a. weak learning), though this advantage might be very small even when gradient descent can achieve arbitrarily high accuracy. Complementing this, we show that without these conditions, gradient descent can in fact learn with small error even when no kernel method, in particular using the tangent kernel, can achieve a non-trivial advantage over random guessing. 

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2. Profiling Pareto Front With Multi-Objective Stein Variational Gradient Descent

   Xingchao Liu; Xin Tong; Qiang Liu (January 2021, Advances in neural information processing systems)

   Finding diverse and representative Pareto solutions from the Pareto front is a key challenge in multi-objective optimization (MOO). In this work, we propose a novel gradient-based algorithm for profiling Pareto front by using Stein variational gradient descent (SVGD). We also provide a counterpart of our method based on Langevin dynamics. Our methods iteratively update a set of points in a parallel fashion to push them towards the Pareto front using multiple gradient descent, while encouraging the diversity between the particles by using the repulsive force mechanism in SVGD, or diffusion noise in Langevin dynamics. Compared with existing gradient-based methods that require predefined preference functions, our method can work efficiently in high dimensional problems, and can obtain more diverse solutions evenly distributed in the Pareto front. Moreover, our methods are theoretically guaranteed to converge to the Pareto front. We demonstrate the effectiveness of our method, especially the SVGD algorithm, through extensive experiments, showing its superiority over existing gradient-based algorithms. 

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3. Accelerated primal-dual methods for convex-strongly-concave saddle point problems

   Khalafi, Mohammad; Boob, Digvijay (July 2023, Proceedings of Machine Learning Research)

   We investigate a primal-dual (PD) method for the saddle point problem (SPP) that uses a linear approximation of the primal function instead of the standard proximal step, resulting in a linearized PD (LPD) method. For convex-strongly concave SPP, we observe that the LPD method has a suboptimal dependence on the Lipschitz constant of the primal function. To fix this issue, we combine features of Accelerated Gradient Descent with the LPD method resulting in a single-loop Accelerated Linearized Primal-Dual (ALPD) method. ALPD method achieves the optimal gradient complexity when the SPP has a semi-linear coupling function. We also present an inexact ALPD method for SPPs with a general nonlinear coupling function that maintains the optimal gradient evaluations of the primal parts and significantly improves the gradient evaluations of the coupling term compared to the ALPD method. We verify our findings with numerical experiments. 

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4. A mean-field analysis of two-player zero-sum games

   Domingo-Enrich, Carles; Jelassi, S; Mensch, A; Rotskoff, G; Bruna, J (December 2020, Advances in neural information processing systems)

   null (Ed.)

   Finding Nash equilibria in two-player zero-sum continuous games is a central problem in machine learning, e.g. for training both GANs and robust models. The existence of pure Nash equilibria requires strong conditions which are not typically met in practice. Mixed Nash equilibria exist in greater generality and may be found using mirror descent. Yet this approach does not scale to high dimensions. To address this limitation, we parametrize mixed strategies as mixtures of particles, whose positions and weights are updated using gradient descent-ascent. We study this dynamics as an interacting gradient flow over measure spaces endowed with the Wasserstein-Fisher-Rao metric. We establish global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic. We prove a law of large numbers that relates particle dynamics to mean-field dynamics. Our method identifies mixed equilibria in high dimensions and is demonstrably effective for training mixtures of GANs. 

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5. Min-Max Entropy Inverse RL of Multiple Tasks

   Arora, Saurabh; Doshi, Prashant; Banerjee, Bikramjit (July 2021, IEEE International Conference on Robotics and Automation)

   null (Ed.)

   Multi-task IRL recognizes that expert(s) could be switching between multiple ways of solving the same problem, or interleaving demonstrations of multiple tasks. The learner aims to learn the reward functions that individually guide these distinct ways. We present a new method for multi-task IRL that generalizes the well-known maximum entropy approach by combining it with a Dirichlet process based minimum entropy clustering of the observed data. This yields a single nonlinear optimization problem, called MinMaxEnt Multi-task IRL (MME-MTIRL), which can be solved using the Lagrangian relaxation and gradient descent methods. We evaluate MME- MTIRL on the robotic task of sorting onions on a processing line where the expert utilizes multiple ways of detecting and removing blemished onions. The method is able to learn the underlying reward functions to a high level of accuracy and it improves on the previous approaches. 

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