5 citations · 12 across the 11 of their papers we have counts for
14 papers · 1 filter
High Probability Complexity Bounds of Trust-Region Stochastic Sequential Quadratic Programming with Heavy-Tailed Noise
Yuchen Fang, Javad Lavaei, Sen Na
In this paper, we consider nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We propose a Trust-Region Stochastic Sequential Quadr…
The landscape of deterministic and stochastic optimal control problems: One-shot Optimization versus Dynamic Programming
Jihun Kim, Yuhao Ding, Yingjie Bi +1
Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global o…
Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses
Ziye Ma, Ying Chen, Javad Lavaei +1
Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points…
Algorithmic Regularization in Tensor Optimization: Towards a Lifted Approach in Matrix Sensing
Ziye Ma, Javad Lavaei, Somayeh Sojoudi
Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine t…
Factorization Approach for Low-complexity Matrix Completion Problems: Exponential Number of Spurious Solutions and Failure of Gradient Methods
Baturalp Yalcin, Haixiang Zhang, Javad Lavaei +1
It is well-known that the Burer-Monteiro (B-M) factorization approach can efficiently solve low-rank matrix optimization problems under the RIP condition. It is natural to ask whet…
General Low-rank Matrix Optimization: Geometric Analysis and Sharper Bounds
Haixiang Zhang, Yingjie Bi, Javad Lavaei
This paper considers the global geometry of general low-rank minimization problems via the Burer-Monterio factorization approach. For the rank- case, we prove that there is no s…