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Classical global convergence results for first-order methods rely on uniform smoothness and the \L{}ojasiewicz inequality.
Une propriété topologique des sous-ensembles analytiques réels
Łojasiewicz, S · 1963
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Gradient methods for minimizing functionals
Polyak, B. T · 1963
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Problem complexity and method efficiency in optimization
Nemirovski, A. S. and Yudin, D. B · 1983
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On gradients of functions definable in o-minimal structures
Kurdyka, K · 1998
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Policy gradient methods for reinforcement learning with function approximation
Sutton, R. S., McAllester, D. A., Singh, S. P., and Mansour, Y · 2000
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Approximately optimal approximate reinforcement learning
Kakade, S. and Langford, J · 2002
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Introductory lectures on convex optimization: A basic course , volume 87
Nesterov, Y · 2003
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Convex optimization: Algorithms and complexity
Bubeck, S · 2014
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Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
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Beyond convexity: Stochastic quasi-convex optimization
Hazan, E., Levy, K., and Shalev-Shwartz, S · 2015
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Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition
Karimi, H., Nutini, J., and Schmidt, M · 2016
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A convergence theory for deep learning via over-parameterization
Allen-Zhu, Z., Li, Y., and Song, Z · 2019
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Provably efficient maximum entropy exploration
Why gradient clipping accelerates training: A theoretical justification for adaptivity
Zhang, J., He, T., Sra, S., and Jadbabaie, A · 2019
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Optimality and approximation with policy gradient methods in markov decision processes
Agarwal, A., Kakade, S. M., Lee, J. D., and Mahajan, G · 2020
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A note on the linear convergence of policy gradient methods
Bhandari, J. and Russo, D · 2020
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Fast global convergence of natural policy gradient methods with entropy regularization
Cen, S., Cheng, C., Chen, Y., Wei, Y., and Chi, Y · 2020
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Gradient descent on neural networks typically occurs at the edge of stability
Cohen, J., Kaur, S., Li, Y., Kolter, J. Z., and Talwalkar, A · 2021
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Hazan, E., Kakade, S., Singh, K., and Van Soest, A · 2019
Cited alongside, same era.
Accelerating rescaled gradient descent: Fast optimization of smooth functions
Wilson, A., Mackey, L., and Wibisono, A · 2019
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Escaping the gravitational pull of softmax
Mei, J., Xiao, C., Dai, B., Li, L., Szepesvári, C., and Schuurmans, D
Cited in the paper.
On the global convergence rates of softmax policy gradient methods
Mei, J., Xiao, C., Szepesvari, C., and Schuurmans, D
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Softmax policy gradient methods can take exponential time to converge
Li, G., Wei, Y., Chi, Y., Gu, Y., and Chen, Y · 2021
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