A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper improves analysis of clipping algorithms for non-convex optimization.
problem Improving convergence analysis of clipping algorithms for non-convex optimization.
method Develops a general framework to study clipping algorithms, including momentum methods, and provides convergence analysis in deterministic and stochastic settings.
result Demonstrates that clipping methods can maintain efficiency even in highly non-smooth regions.
Existing approaches for training neural networks with user-level differential privacy (e.g., DP Federated Averaging) in federated learning (FL) settings involve bounding the contribution of each user's model update by clipping it to some constant value. However there is no good a priori setting of the clipping norm acr…
Clip21 improves convergence of gradient-clipped methods in DP settings.
problem Gradient clipping introduces bias in distributed training, causing convergence issues.
method Clip21 designs an error feedback mechanism to mitigate bias in gradient-clipped methods.
result Clip21 converges at the same rate as distributed gradient descent, improving from previous $\mathcal{O}\left(\frac{1}{\sqrt{K}}
ight)$ to $\mathcal{O}\left(\frac{1}{K}
ight)$.
Paper proves convergence for private FL on non-Lipschitz convex objectives using normalization instead of clipping.
problem Lack of convergence results for differentially private federated learning with non-Lipschitz objectives.
method Developed a convergence result for private FL on smooth convex objectives without assuming Lipschitzness, using normalization instead of clipping.
result Normalization-based private FL algorithm converges better than clipping-based counterpart on smooth convex functions.
Many continuous control tasks have bounded action spaces. When policy gradient methods are applied to such tasks, out-of-bound actions need to be clipped before execution, while policies are usually optimized as if the actions are not clipped. We propose a policy gradient estimator that exploits the knowledge of action…
In importance sampling (IS)-based reinforcement learning algorithms such as Proximal Policy Optimization (PPO), IS weights are typically clipped to avoid large variance in learning. However, policy update from clipped statistics induces large bias in tasks with high action dimensions, and bias from clipping makes it di…
The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from e…
We establish the second part of Milnor's conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.
A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in the isometry group of hyperbolic 3-space, with fundamental domain a geodesic simplex (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23 non-cocompact examp…
We introduce the non-pure versions of simplicial balls and spheres with minimum number of vertices. These are a special type of non-homogeneous balls and spheres (NH-balls and NH-spheres) satisfying a minimality condition on the number of maximal simplices. The main result is that minimal NH-balls and NH-spheres are pr…
In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples of π, is it true that its volume is a rational multiple of the volu…
We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a low-rank matrix from various information deficits by using the principle of low-ran…