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An Exponential Tail bound for Lq Stable Learning Rules

Karim T. Abou-Moustafa, Csaba Szepesvári
2019 International Conference on Algorithmic Learning Theory  
As an illustration we derive exponential tail bounds for ridge regression with unbounded responses, where we show how stability changes with the tail behavior of the response variables.  ...  tail bound for the concentration of the estimated risk of a hypothesis returned by a general learning rule, where the estimated risk is expressed in terms of either the resubstitution estimate (empirical  ...  Acknowledgments We would like to thank our ALT Reviewers and AC for their thoughtful comments which helped us improve the presentation of our manuscript.  ... 
dblp:conf/alt/Abou-MoustafaS19 fatcat:mbt7faon6jfdbnqxyqotbgprru

An Exponential Tail Bound for Lq Stable Learning Rules. Application to k-Folds Cross-Validation

Karim T. Abou-Moustafa, Csaba Szepesvári
2018 International Symposium on Artificial Intelligence and Mathematics  
In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general function of n independent random variables.  ...  by a general learning rule.  ...  For a stable learning rule with small higher order moments, the bound is tightest for the deleted estimate (k = n).  ... 
dblp:conf/isaim/Abou-MoustafaS18 fatcat:gey2t2v5hjgfhlhbkywsqtbvtm

An Exponential Efron-Stein Inequality for Lq Stable Learning Rules [article]

Karim Abou-Moustafa, Csaba Szepesvari
2019 arXiv   pre-print
As an illustration, we derive exponential tail bounds for ridge regression with unbounded responses, where we show how stability changes with the tail behavior of the response variables.  ...  tail bound for the concentration of the estimated risk of a hypothesis returned by a general learning rule, where the estimated risk is expressed in terms of either the resubstitution estimate (empirical  ...  Acknowledgments We would like to thank our ALT Reviewers and AC for their thoughtful comments which helped us improve the presentation of our manuscript.  ... 
arXiv:1903.05457v2 fatcat:lpk4km4g5facthtpdzlikonkzu

Learning Linear-Quadratic Regulators Efficiently with only √(T) Regret [article]

Alon Cohen, Tomer Koren, Yishay Mansour
2019 arXiv   pre-print
We present the first computationally-efficient algorithm with O(√(T)) regret for learning in Linear Quadratic Control systems with unknown dynamics.  ...  By that, we resolve an open question of Abbasi-Yadkori and Szepesvári (2011) and Dean, Mania, Matni, Recht, and Tu (2018).  ...  AC thanks Lotem Peled for her assistance and support.  ... 
arXiv:1902.06223v2 fatcat:matn7ew4szbnnjwh3d7t3jbzoq

Gradient Descent Maximizes the Margin of Homogeneous Neural Networks [article]

Kaifeng Lyu, Jian Li
2020 arXiv   pre-print
results for homogeneous smooth neural networks.  ...  Finally, as margin is closely related to robustness, we discuss potential benefits of training longer for improving the robustness of the model.  ...  Lee, Zhiyuan Li, Tengyu Ma, Ruosong Wang for helpful discussions.  ... 
arXiv:1906.05890v4 fatcat:ii6nhr3qkzhatirdhluhiqjdhi

RL-QN: A Reinforcement Learning Framework for Optimal Control of Queueing Systems [article]

Bai Liu, Qiaomin Xie, Eytan Modiano
2022 arXiv   pre-print
In this work, we consider using model-based reinforcement learning (RL) to learn the optimal control policy for queueing networks so that the average job delay (or equivalently the average queue backlog  ...  To overcome this difficulty, we propose a new algorithm, called Reinforcement Learning for Queueing Networks (RL-QN), which applies model-based RL methods over a finite subset of the state space, while  ...  By applying similar techniques as Lemma 1 in [8] , we establish an upper bound for the tail probability of Lyapunov values, which decays exponentially. The detailed proof is given in Appendix C.  ... 
arXiv:2011.07401v2 fatcat:nfqa7mfnz5b2vmduzoekwrg5ie

Reinforcement Learning with Fast Stabilization in Linear Dynamical Systems [article]

Sahin Lale, Kamyar Azizzadenesheli, Babak Hassibi, Anima Anandkumar
2022 arXiv   pre-print
We also show that the regret of the proposed algorithm has only a polynomial dependence in the problem dimensions, which gives an exponential improvement over the prior methods.  ...  In this work, we study model-based reinforcement learning (RL) in unknown stabilizable linear dynamical systems.  ...  upper bound suffers from an exponential dependence in the LQR model dimensions.  ... 
arXiv:2007.12291v2 fatcat:eiziw7ps7zaejmvyh365mi7f3m

Statistical mechanics of learning from examples

H. S. Seung, H. Sompolinsky, N. Tishby
1992 Physical Review A. Atomic, Molecular, and Optical Physics  
We show that for smooth networks, i.e. , those with continuously varying weights and smooth transfer functions, the generalization curve asymptotically obeys an inverse power law.  ...  Learning of realizable rules as well as of unrealizable rules is considered. In the latter case, the target rule cannot be perfectly realized by a network of the given architecture.  ...  Using Eqs. (4.14), (4.15), and (4.20), the annealed has an exponential tail.  ... 
doi:10.1103/physreva.45.6056 pmid:9907706 fatcat:octqz2qh7zgnnhl6ztv4nc4osq

Federated Learning with Buffered Asynchronous Aggregation [article]

John Nguyen, Kshitiz Malik, Hongyuan Zhan, Ashkan Yousefpour, Michael Rabbat, Mani Malek, Dzmitry Huba
2022 arXiv   pre-print
Scalability and privacy are two critical concerns for cross-device federated learning (FL) systems.  ...  However, aggregating individual client updates is incompatible with Secure Aggregation, which could result in an undesirable level of privacy for the system.  ...  We would like to also thank the anonymous reviewers for their insightful feedback.  ... 
arXiv:2106.06639v4 fatcat:cmpki6uduzhbnbty6gob7mld5a

MPC for Humanoid Gait Generation: Stability and Feasibility [article]

Nicola Scianca, Daniele De Simone, Leonardo Lanari, Giuseppe Oriolo
2019 arXiv   pre-print
We present IS-MPC, an intrinsically stable MPC framework for humanoid gait generation which incorporates an explicit stability constraint in the formulation.  ...  Several possible options for the tail are discussed, and each of them is shown to correspond to a specific terminal constraint.  ...  Abderrahmane Kheddar of CNRS for hosting Daniele De Simone at LIRMM in Montpellier and allowing him to perform experiments on the HRP-4 humanoid robot.  ... 
arXiv:1901.08505v2 fatcat:zq23dtk57vdrjahfrc2nwauz2i

Logarithmic Regret for Learning Linear Quadratic Regulators Efficiently [article]

Asaf Cassel
2020 arXiv   pre-print
On the other hand, we give a lower bound that shows that when the latter condition is violated, square root regret is unavoidable.  ...  We consider the problem of learning in Linear Quadratic Control systems whose transition parameters are initially unknown.  ...  Regret bounds for the adaptive control of linear quadratic systems. In Proceedings of the 24th Annual Conference on Learning Theory, pages 1-26, 2011.  ... 
arXiv:2002.08095v2 fatcat:7ojyorwaufbyrjxa6hgsmt7vta

Spatial mixing and the random-cluster dynamics on lattices [article]

Reza Gheissari, Alistair Sinclair
2022 arXiv   pre-print
An important paradigm in the understanding of mixing times of Glauber dynamics for spin systems is the correspondence between spatial mixing properties of the models and bounds on the mixing time of the  ...  initializations is exponentially large).  ...  R.G. thanks the Miller Institute for Basic Research in Science for its support. The research of A.S. is supported in part by NSF grant CCF-1815328.  ... 
arXiv:2207.11195v1 fatcat:gslky3lyjrg4zjhlzcq5jundxy

On almost sure limit theorems for detecting long-range dependent, heavy-tailed processes [article]

Michael A. Kouritzin
2020 arXiv   pre-print
The decay of the coefficients c_l^(r) as |l|→∞, can be slow enough for {x_k^(r)} to have long memory while {d_k} can have heavy tails.  ...  The long-range dependence and heavy tails for {d_k} are handled simultaneously and a decoupling property shows the convergence rate is dictated by the worst of long-range dependence and heavy tails, but  ...  Their tails are not exponentially bounded and estimating tail decay is a common problem.  ... 
arXiv:2007.06083v2 fatcat:wj5ymc4cg5a5tk2deagquhb7je

Les Houches 2019 Physics at TeV Colliders: New Physics Working Group Report [article]

G. Brooijmans, A. Buckley, S. Caron, A. Falkowski, B. Fuks, A. Gilbert, W. J. Murray, M. Nardecchia, J. M. No, R. Torre, T. You, G. Zevi Della Porta (+74 others)
2020 arXiv   pre-print
Benefits of machine learning for both the search for new physics and the interpretation of these searches are also presented.  ...  This report presents the activities of the 'New Physics' working group for the 'Physics at TeV Colliders' workshop (Les Houches, France, 10--28 June, 2019).  ...  We explain the main features, the data format and describe the use of this data for an upcoming data challenge. The data is available at the webpage https://www.phenoMLdata.org.  ... 
arXiv:2002.12220v1 fatcat:meayxp222fdf7mb3j5faa6unwi

2021 Index IEEE Transactions on Systems, Man, and Cybernetics: Systems Vol. 51

2021 IEEE Transactions on Systems, Man & Cybernetics. Systems  
The Author Index contains the primary entry for each item, listed under the first author's name.  ...  ., +, TSMC June 2021 3608-3616 Asymmetric Bounded Neural Control for an Uncertain Robot by State Feedback and Output Feedback.  ...  ., +, TSMC Oct. 2021 6159-6169 Asymmetric Bounded Neural Control for an Uncertain Robot by State Feedback and Output Feedback.  ... 
doi:10.1109/tsmc.2021.3136054 fatcat:b5hcsfwjw5hllpenqmaq6wpke4
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