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Register a new userFastAdaBelief: Improving Convergence Rate for Belief-based Adaptive Optimizers by Exploiting Strong Convexity
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AdaBelief, one of the current best optimizers, demonstrates superior generalization ability compared to the popular Adam algorithm by viewing the exponential moving average of observed gradients. AdaBelief is theoretically appealing in that it has a data-dependent $O(sqrt{T})$ regret bound when objective functions are convex, where $T$ is a time horizon. It remains however an open problem whether the convergence rate can be further improved without sacrificing its generalization ability. %on how to exploit strong convexity to further improve the convergence rate of AdaBelief. To this end, we make a first attempt in this work and design a novel optimization algorithm called FastAdaBelief that aims to exploit its strong convexity in order to achieve an even faster convergence rate. In particular, by adjusting the step size that better considers strong convexity and prevents fluctuation, our proposed FastAdaBelief demonstrates excellent generalization ability as well as superior convergence. As an important theoretical contribution, we prove that FastAdaBelief attains a data-dependant $O(log T)$ regret bound, which is substantially lower than AdaBelief. On the empirical side, we validate our theoretical analysis with extensive experiments in both scenarios of strong and non-strong convexity on three popular baseline models. Experimental results are very encouraging: FastAdaBelief converges the quickest in comparison to all mainstream algorithms while maintaining an excellent generalization ability, in cases of both strong or non-strong convexity. FastAdaBelief is thus posited as a new benchmark model for the research community.
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In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatio-temporal data analysis. The convergence rate is analyzed in terms of both in-sample and out-of-sample predictive accuracies. It is shown that a near optimal rate is achieved without any strong convexity of the observation. Moreover, we show that the method has adaptivity to the unknown rank of the true tensor, that is, the near optimal rate depending on the true rank is achieved even if it is not known a priori.
Training neural networks with large batch is of fundamental significance to deep learning. Large batch training remarkably reduces the amount of training time but has difficulties in maintaining accuracy. Recent works have put forward optimization methods such as LARS and LAMB to tackle this issue through adaptive layer-wise optimization using trust ratios. Though prevailing, such methods are observed to still suffer from unstable and extreme trust ratios which degrades performance. In this paper, we propose a new variant of LAMB, called LAMBC, which employs trust ratio clipping to stabilize its magnitude and prevent extreme values. We conducted experiments on image classification tasks such as ImageNet and CIFAR-10 and our empirical results demonstrate promising improvements across different batch sizes.
We introduce the technique of adaptive discretization to design an efficient model-based episodic reinforcement learning algorithm in large (potentially continuous) state-action spaces. Our algorithm is based on optimistic one-step value iteration extended to maintain an adaptive discretization of the space. From a theoretical perspective we provide worst-case regret bounds for our algorithm which are competitive compared to the state-of-the-art model-based algorithms. Moreover, our bounds are obtained via a modular proof technique which can potentially extend to incorporate additional structure on the problem. From an implementation standpoint, our algorithm has much lower storage and computational requirements due to maintaining a more efficient partition of the state and action spaces. We illustrate this via experiments on several canonical control problems, which shows that our algorithm empirically performs significantly better than fixed discretization in terms of both faster convergence and lower memory usage. Interestingly, we observe empirically that while fixed-discretization model-based algorithms vastly outperform their model-free counterparts, the two achieve comparable performance with adaptive discretization.
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