AbstractA random variable ( RV ) X is given aminimum selling price(S ) $ $ S_U \left ( X \right ) : = \mathop { \sup } \limits_x \left\ { { x + EU\left ( { X - x } \right ) } \right\}$$ and amaximum buying price(B ) $ $ B_p \left ( X \right ) : = \mathop { \inf } \limits_x \left\ { { x + EP\left ( { X - x } \right ) } \right\}$$ whereU ( · ) andP ( · ) are appropriate functions . These prices are derived from considerations ofstochastic optimization with recourse , and are calledrecourse certainty equivalents ( RCE 's ) of X. Both RCE 's compute the “ value ” of a RV as an optimization problem , and both problems ( S ) and ( B ) have meaningful dual problems , stated in terms of theCsiszár φ-divergence $ $ I_\phi \left ( { p , q } \right ) : = \sum\limits_{i = 1}^n { q_i \phi \left ( { \frac{{p_i } } { { q_i } } } \right ) } $ $ a generalized entropy function , measuring the distance between RV 's with probability vectors p and q . The RCESU was studied elsewhere , and applied to production , investment and insurance problems . \limits_z \ { z + E_Z \upsilon ( Z - z)\ } , $ $ wherev ( · ) is the decision maker'svalue-risk function . This CE is derived from considerations ofstochastic optimization with recourse , and is calledrecourse certainty equivalent ( RCE ) . We study ( i ) the properties of the RCE , ( ii ) the recoverability ofv ( · ) fromSv ( · ) ( in terms of the rate of change in risk ) , ( iii ) comparison with the “ classical CE”u−1Eu ( · ) inexpected utility ( EU ) theory , ( iv ) relation to risk-aversion , ( v ) connection with Machina'sgeneralized expected utility theory , and its use to explain theAllais paradox and other decision theoretic paradoxes , and ( vi ) applications to models ofproduction under price uncertainty , investment in risky and safe assets andinsurance . The stochastic model is utilized to obtain the optimal control laws ; the resultant non-linear constrained minimization problem is solved by an Augmented Lagrangian approach , using a Quasi-Newton technique . The results of the stochastic optimization analysis indicate that significant reductions in performance degradation may be achieved with respect to the solutions provided by the classical deterministic approach . In this paper , we address a specific safety formulation , where danger is encoded in the reward signal and the learning agent is constrained to never worsen its performance . By studying actor-only policy gradient from a stochastic optimization perspective , we establish improvement guarantees for a wide class of parametric policies , generalizing existing results on Gaussian policies . This , together with novel upper bounds on the variance of policy gradient estimators , allows to identify those meta-parameter schedules that guarantee monotonic improvement with high probability . To understand customer decisions , we formulate the problem of determining hourly battery charging and discharge schedules to minimize expected net costs , defined as energy purchase costs minus energy export rebates and DR payments , over a sufficiently long time horizon ( e.g. , a year ) . The complexity of this stochastic optimization problem grows exponentially with the time horizon considered . To obtain computationally tractable solutions , we propose using multistage model predictive control with scenario sampling . To optimally size the BESS from an economic perspective , the tradeoff between BESS investment costs , lifetime , and revenue from utility bill savings along with microgrid ancillary services must be taken into account . The optimal size of a BESS is solved via a stochastic optimization problem considering wholesale market pricing . A stochastic model is used to schedule arbitrage services for energy storage based on the forecasted energy market pricing while accounting for BESS cost trends , the variability of renewable energy resources , and demand prediction . The system power consumption , which includes the local execution power and the offloading transmission power , is designated as the main system performance index . First , we formulate the power consumption minimization problem with the battery queue stability and QoS constraints as a stochastic optimization programming , which is difficult to solve due to the time-coupling constraints . Then , we adopt the Lyapunov optimization approach to tackle the problem by reformulating it into a problem with relaxed queue stability constraints . The scenario-based stochastic modelling is also included to deal with uncertainty in loading . The expressed stochastic optimization programming minimizes the daily energy cost in building and determines the optimal charging-discharging pattern for both thermal and electrical storage systems at the same time . The results demonstrate that electrical energy storage system reduces the cost about 15 % , the thermal energy storage system decreases the cost about 17 % , and coordinated thermal-electrical energy storage system reduces the cost about 34 % . It is built upon a 4-D time-continuous affine motion model which is capable of compactly describing highly non-periodic motion patterns . A stochastic optimization scheme is derived which minimizes the error between the measured projection data and the forward projection of the motion compensated reconstruction . For evaluation , the algorithm is applied to 5 datasets of the left coronary arteries of patients that have ignored the breath hold command and/or had arrhythmic heart signals during the data acquisition . This paper presents a robust method for groupwise affine registration based on the RASL algorithm [ 1 ] that formulates the registration problem as a sparse and low-rank decomposition . We adapt the RASL algorithm for the alignment of 3D image data and introduce a stochastic optimization scheme to enable the computational tractability . Further , a normalization scheme generates more plausible and unique transformations . In this paper , we propose the MUSE approach to tackle this problem . Specifically , by directly considering the concerned performance measure , we develop a convex optimization formulation and provide an efficient stochastic optimization solution for a large variety of multi-label performance measures . Experiments show that MUSE is able to obtain smaller multi-label ensembles , whilst achieving better or at least comparable performance in terms of the concerned performance measure . In this paper , the mode-independent control problem of singular Markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint . A new kind of mode-independent H∞ controller satisfying a minimum variance approximation is constructed , whose gain is composed of some mode-dependent control gains . Abstract Many issues in the cloud can be transformed into optimization problems , where data is of high dimension and randomness . Thus , stochastic optimizing is a key to Autonomous Cloud . And one of the most significant discussions in this field is how to adapt the learning rate and convergent path dynamically . The algorithm that the grammar uses to generate trees and strings in the language is characterized in terms of a transition - based algorithm , which is outlined in the next section . In the section after that , the semantics of the parameters that are used to turn this into a stochastic algorithm that generates pairs of trees and strings are discussed . section : Top - down Parsing and Generation In the batch setting where each training step is based on the entire training set , we would use the whole set to normalize activations . However , this is impractical when using stochastic optimization . Therefore , we make the second simplification : since we use mini - batches in stochastic gradient training , each mini - batch produces estimates of the mean and variance of each activation . These adaptive methods can in fact be treated as relaxations of NGD with only a slight difference lying in the square root of the denominator in the update rules . Skeptical about the effect of such difference , we design a new algorithm --- AdaSqrt , which removes the square root in the denominator and scales the learning rate by sqrt(T ) . Surprisingly , our new algorithm is comparable to various first-order methods(such as SGD and Adam ) on MNIST and even beats Adam on CIFAR-10 ! We design a new algorithm , called Partially adaptive momentum estimation method ( Padam ) , which unifies the Adam/Amsgrad with SGD to achieve the best from both worlds . Experiments on standard benchmarks show that Padam can maintain fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks . These results would suggest practitioners pick up adaptive gradient methods once again for faster training of deep neural networks . Despite the wide applications of Adam in reinforcement learning ( RL ) , the theoretical convergence of Adam-type RL algorithms has not been established . This paper provides the first such convergence analysis for two fundamental RL algorithms of policy gradient ( PG ) and temporal difference ( TD ) learning that incorporate AMSGrad updates ( a standard alternative of Adam in theoretical analysis ) , referred to as PG-AMSGrad and TD-AMSGrad , respectively . Moreover , our analysis focuses on Markovian sampling for both algorithms . We show that under general nonlinear function approximation , PG-AMSGrad with a constant stepsize converges to a neighborhood of a stationary point at the rate of $ \mathcal{O}(1/T)$ ( where $ T$ denotes the number of iterations ) , and with a diminishing stepsize converges exactly to a stationary point at the rate of $ \mathcal{O}(\log^2 T/\sqrt{T})$. Furthermore , under linear function approximation , TD-AMSGrad with a constant stepsize converges to a neighborhood of the global optimum at the rate of $ \mathcal{O}(1/T)$ , and with a diminishing stepsize converges exactly to the global optimum at the rate of $ \mathcal{O}(\log T/\sqrt{T})$. Our study develops new techniques for analyzing the Adam-type RL algorithms under Markovian sampling . In this paper we have analyzed RMSProp , originally proposed for the training of deep neural networks , in the context of online convex optimization and show $ \sqrt{T}$-type regret bounds . Moreover , we propose two variants SC-Adagrad and SC-RMSProp for which we show logarithmic regret bounds for strongly convex functions . Finally , we demonstrate in the experiments that these new variants outperform other adaptive gradient techniques or stochastic gradient descent in the optimization of strongly convex functions as well as in training of deep neural networks . Theoretically , we develop an algorithm ( Optimistic Stochastic Gradient , OSG ) for solving a class of non-convex non-concave min-max problem and establish $ O(\epsilon^{-4})$ complexity for finding $ \epsilon$-first-order stationary point , in which only one stochastic first-order oracle is invoked in each iteration . An adaptive variant of the proposed algorithm ( Optimistic Adagrad , OAdagrad ) is also analyzed , revealing an \emph{improved } adaptive complexity $ \widetilde{O}\left(\epsilon^{-\frac{2}{1-\alpha}}\right)$~\footnote{Here $ \widetilde{O}(\cdot)$ compresses a logarithmic factor of $ \epsilon$. } , where $ \alpha$ characterizes the growth rate of the cumulative stochastic gradient and $ 0\leq \alpha\leq 1/2$. To the best of our knowledge , this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization . Empirically , our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training . While the most common approach to solving these problems is to apply stochastic gradient descent ( SGD ) or similar methods such as AdaGrad and Adam , which involve estimating a stochastic gradient from a small number of Monte Carlo samples computed at each iteration , we show that for this category of problems it is possible to achieve faster asymptotic convergence rates using an increasing number of samples per iteration instead , a strategy we call increasing precision ( IP ) . We then improve pre-asymptotic convergence by introducing a hybrid approach that combines the qualities of increasing precision and otherwise " constant " precision , resulting in methods such as the IP-SGD hybrid and IP-AdaGrad hybrid , essentially by modifying their gradient estimators to have an equivalent effect to increasing precision . Finally , we observe that , in some problems , incorporating a Gauss-Newton preconditioner to the IP-SGD hybrid method can provide much better convergence than employing a Quasi-Newton approach or covariance-preconditioning as in AdaGrad or Adam . We demonstrate the power of this decoupling by obtaining generalized algorithms and improved regret bounds for the so-called “ adaptive optimistic online learning ” setting . In addition , we simplify and extend a large body of previous work , including several various AdaGrad formulations , composite-objective and implicit-update algorithms . In all cases , the results follow as simple corollaries within few lines of algebra . Four different optimizers are used with the TF-CNN , Adagrad , ProximalAdagrad , Adam , and RMSProp to achieve accurate classification . The re-sult demonstrates that the loss value of the Adam and RMSProp optimizers was lower than the Adagrad and ProximalAdagrad optimizers . The classification accuracy using Adam optimizer is 95.8 % , while it reaches 100 % when using RMSProp optimizer . In this paper , we propose an efficient parallel framework for translating embedding methods , called ParTrans-X , which enables the methods to be paralleled without locks by utilizing the distinguished structures of knowledge graphs . Experiments on two datasets with three typical translating embedding methods , i.e. , TransE [ 3 ] , TransH [ 19 ] , and a more efficient variant TransE- AdaGrad [ 11 ] validate that ParTrans-X can speed up the training process by more than an order of magnitude . The O ( log T √ T ) nonasymptotic convergence rates of AdaHB and AdaNAG in non-convex stochastic setting are also jointly characterized by leveraging a newly developed unified formulation of these two momentum mechanisms . In particular , when momentum term vanishes we obtain convergence rate of coordinate-wise AdaGrad in non-convex stochastic setting as a byproduct . Moreover , comparisons have been made between AdaHB , AdaNAG , Adam and RMSProp , which , to a certain extent , explains the reasons why Adam and RMSProp are divergent . In particular , when momentum term vanishes we obtain convergence rate of coordinate-wise AdaGrad in non-convex stochastic setting as a byproduct . Additionally , each actor / learner keeps a running average and standard deviation of the absolute DQN loss for the data it sees and discards gradients with absolute loss higher than the mean plus several standard deviations . Finally , we used the AdaGrad update rule . section : Experiments We repeat the above iterations until stopping . We adopt AdaGrad duchi2011adaptive to dynamically compute the learning rates for each iteration . Since the source and target tasks might have different convergence rates , we do early stopping on the target task performance . λ is set as 0.001 based on the validation . Since the input is sparse , we use Adagrad [ reference ] for optimization . We repeat this evaluation 10 times and report mean accuracy .
AbstractA random variable ( RV ) X is given aminimum selling price(S ) $ $ S_U \left ( X \right ) : = \mathop { \sup } \limits_x \left\ { { x + EU\left ( { X - x } \right ) } \right\}$$ and amaximum buying price(B ) $ $ B_p \left ( X \right ) : = \mathop { \inf } \limits_x \left\ { { x + EP\left ( { X - x } \right ) } \right\}$$ whereU ( · ) andP ( · ) are appropriate functions . These prices are derived from considerations ofstochastic optimization with recourse , and are calledrecourse certainty equivalents ( RCE 's ) of X. Both RCE 's compute the “ value ” of a RV as an optimization problem , and both problems ( S ) and ( B ) have meaningful dual problems , stated in terms of theCsiszár φ-divergence $ $ I_\phi \left ( { p , q } \right ) : = \sum\limits_{i = 1}^n { q_i \phi \left ( { \frac{{p_i } } { { q_i } } } \right ) } $ $ a generalized entropy function , measuring the distance between RV 's with probability vectors p and q . The RCESU was studied elsewhere , and applied to production , investment and insurance problems .
\limits_z \ { z + E_Z \upsilon ( Z - z)\ } , $ $ wherev ( · ) is the decision maker'svalue-risk function . This CE is derived from considerations ofstochastic optimization with recourse , and is calledrecourse certainty equivalent ( RCE ) . We study ( i ) the properties of the RCE , ( ii ) the recoverability ofv ( · ) fromSv ( · ) ( in terms of the rate of change in risk ) , ( iii ) comparison with the “ classical CE”u−1Eu ( · ) inexpected utility ( EU ) theory , ( iv ) relation to risk-aversion , ( v ) connection with Machina'sgeneralized expected utility theory , and its use to explain theAllais paradox and other decision theoretic paradoxes , and ( vi ) applications to models ofproduction under price uncertainty , investment in risky and safe assets andinsurance .
The stochastic model is utilized to obtain the optimal control laws ; the resultant non-linear constrained minimization problem is solved by an Augmented Lagrangian approach , using a Quasi-Newton technique . The results of the stochastic optimization analysis indicate that significant reductions in performance degradation may be achieved with respect to the solutions provided by the classical deterministic approach .
In this paper , we address a specific safety formulation , where danger is encoded in the reward signal and the learning agent is constrained to never worsen its performance . By studying actor-only policy gradient from a stochastic optimization perspective , we establish improvement guarantees for a wide class of parametric policies , generalizing existing results on Gaussian policies . This , together with novel upper bounds on the variance of policy gradient estimators , allows to identify those meta-parameter schedules that guarantee monotonic improvement with high probability .
To understand customer decisions , we formulate the problem of determining hourly battery charging and discharge schedules to minimize expected net costs , defined as energy purchase costs minus energy export rebates and DR payments , over a sufficiently long time horizon ( e.g. , a year ) . The complexity of this stochastic optimization problem grows exponentially with the time horizon considered . To obtain computationally tractable solutions , we propose using multistage model predictive control with scenario sampling .
To optimally size the BESS from an economic perspective , the tradeoff between BESS investment costs , lifetime , and revenue from utility bill savings along with microgrid ancillary services must be taken into account . The optimal size of a BESS is solved via a stochastic optimization problem considering wholesale market pricing . A stochastic model is used to schedule arbitrage services for energy storage based on the forecasted energy market pricing while accounting for BESS cost trends , the variability of renewable energy resources , and demand prediction .
The system power consumption , which includes the local execution power and the offloading transmission power , is designated as the main system performance index . First , we formulate the power consumption minimization problem with the battery queue stability and QoS constraints as a stochastic optimization programming , which is difficult to solve due to the time-coupling constraints . Then , we adopt the Lyapunov optimization approach to tackle the problem by reformulating it into a problem with relaxed queue stability constraints .
The scenario-based stochastic modelling is also included to deal with uncertainty in loading . The expressed stochastic optimization programming minimizes the daily energy cost in building and determines the optimal charging-discharging pattern for both thermal and electrical storage systems at the same time . The results demonstrate that electrical energy storage system reduces the cost about 15 % , the thermal energy storage system decreases the cost about 17 % , and coordinated thermal-electrical energy storage system reduces the cost about 34 % .
It is built upon a 4-D time-continuous affine motion model which is capable of compactly describing highly non-periodic motion patterns . A stochastic optimization scheme is derived which minimizes the error between the measured projection data and the forward projection of the motion compensated reconstruction . For evaluation , the algorithm is applied to 5 datasets of the left coronary arteries of patients that have ignored the breath hold command and/or had arrhythmic heart signals during the data acquisition .
This paper presents a robust method for groupwise affine registration based on the RASL algorithm [ 1 ] that formulates the registration problem as a sparse and low-rank decomposition . We adapt the RASL algorithm for the alignment of 3D image data and introduce a stochastic optimization scheme to enable the computational tractability . Further , a normalization scheme generates more plausible and unique transformations .
In this paper , we propose the MUSE approach to tackle this problem . Specifically , by directly considering the concerned performance measure , we develop a convex optimization formulation and provide an efficient stochastic optimization solution for a large variety of multi-label performance measures . Experiments show that MUSE is able to obtain smaller multi-label ensembles , whilst achieving better or at least comparable performance in terms of the concerned performance measure .
In this paper , the mode-independent control problem of singular Markovian jump systems is firstly studied by exploiting a stochastic optimization viewpoint . A new kind of mode-independent H∞ controller satisfying a minimum variance approximation is constructed , whose gain is composed of some mode-dependent control gains .
Abstract Many issues in the cloud can be transformed into optimization problems , where data is of high dimension and randomness . Thus , stochastic optimizing is a key to Autonomous Cloud . And one of the most significant discussions in this field is how to adapt the learning rate and convergent path dynamically .
The algorithm that the grammar uses to generate trees and strings in the language is characterized in terms of a transition - based algorithm , which is outlined in the next section . In the section after that , the semantics of the parameters that are used to turn this into a stochastic algorithm that generates pairs of trees and strings are discussed . section : Top - down Parsing and Generation
In the batch setting where each training step is based on the entire training set , we would use the whole set to normalize activations . However , this is impractical when using stochastic optimization . Therefore , we make the second simplification : since we use mini - batches in stochastic gradient training , each mini - batch produces estimates of the mean and variance of each activation .
These adaptive methods can in fact be treated as relaxations of NGD with only a slight difference lying in the square root of the denominator in the update rules . Skeptical about the effect of such difference , we design a new algorithm --- AdaSqrt , which removes the square root in the denominator and scales the learning rate by sqrt(T ) . Surprisingly , our new algorithm is comparable to various first-order methods(such as SGD and Adam ) on MNIST and even beats Adam on CIFAR-10 !
We design a new algorithm , called Partially adaptive momentum estimation method ( Padam ) , which unifies the Adam/Amsgrad with SGD to achieve the best from both worlds . Experiments on standard benchmarks show that Padam can maintain fast convergence rate as Adam/Amsgrad while generalizing as well as SGD in training deep neural networks . These results would suggest practitioners pick up adaptive gradient methods once again for faster training of deep neural networks .
Despite the wide applications of Adam in reinforcement learning ( RL ) , the theoretical convergence of Adam-type RL algorithms has not been established . This paper provides the first such convergence analysis for two fundamental RL algorithms of policy gradient ( PG ) and temporal difference ( TD ) learning that incorporate AMSGrad updates ( a standard alternative of Adam in theoretical analysis ) , referred to as PG-AMSGrad and TD-AMSGrad , respectively . Moreover , our analysis focuses on Markovian sampling for both algorithms . We show that under general nonlinear function approximation , PG-AMSGrad with a constant stepsize converges to a neighborhood of a stationary point at the rate of $ \mathcal{O}(1/T)$ ( where $ T$ denotes the number of iterations ) , and with a diminishing stepsize converges exactly to a stationary point at the rate of $ \mathcal{O}(\log^2 T/\sqrt{T})$. Furthermore , under linear function approximation , TD-AMSGrad with a constant stepsize converges to a neighborhood of the global optimum at the rate of $ \mathcal{O}(1/T)$ , and with a diminishing stepsize converges exactly to the global optimum at the rate of $ \mathcal{O}(\log T/\sqrt{T})$. Our study develops new techniques for analyzing the Adam-type RL algorithms under Markovian sampling .
In this paper we have analyzed RMSProp , originally proposed for the training of deep neural networks , in the context of online convex optimization and show $ \sqrt{T}$-type regret bounds . Moreover , we propose two variants SC-Adagrad and SC-RMSProp for which we show logarithmic regret bounds for strongly convex functions . Finally , we demonstrate in the experiments that these new variants outperform other adaptive gradient techniques or stochastic gradient descent in the optimization of strongly convex functions as well as in training of deep neural networks .
Theoretically , we develop an algorithm ( Optimistic Stochastic Gradient , OSG ) for solving a class of non-convex non-concave min-max problem and establish $ O(\epsilon^{-4})$ complexity for finding $ \epsilon$-first-order stationary point , in which only one stochastic first-order oracle is invoked in each iteration . An adaptive variant of the proposed algorithm ( Optimistic Adagrad , OAdagrad ) is also analyzed , revealing an \emph{improved } adaptive complexity $ \widetilde{O}\left(\epsilon^{-\frac{2}{1-\alpha}}\right)$~\footnote{Here $ \widetilde{O}(\cdot)$ compresses a logarithmic factor of $ \epsilon$. } , where $ \alpha$ characterizes the growth rate of the cumulative stochastic gradient and $ 0\leq \alpha\leq 1/2$. To the best of our knowledge , this is the first work for establishing adaptive complexity in non-convex non-concave min-max optimization . Empirically , our experiments show that indeed adaptive gradient algorithms outperform their non-adaptive counterparts in GAN training .
While the most common approach to solving these problems is to apply stochastic gradient descent ( SGD ) or similar methods such as AdaGrad and Adam , which involve estimating a stochastic gradient from a small number of Monte Carlo samples computed at each iteration , we show that for this category of problems it is possible to achieve faster asymptotic convergence rates using an increasing number of samples per iteration instead , a strategy we call increasing precision ( IP ) . We then improve pre-asymptotic convergence by introducing a hybrid approach that combines the qualities of increasing precision and otherwise " constant " precision , resulting in methods such as the IP-SGD hybrid and IP-AdaGrad hybrid , essentially by modifying their gradient estimators to have an equivalent effect to increasing precision . Finally , we observe that , in some problems , incorporating a Gauss-Newton preconditioner to the IP-SGD hybrid method can provide much better convergence than employing a Quasi-Newton approach or covariance-preconditioning as in AdaGrad or Adam .
We demonstrate the power of this decoupling by obtaining generalized algorithms and improved regret bounds for the so-called “ adaptive optimistic online learning ” setting . In addition , we simplify and extend a large body of previous work , including several various AdaGrad formulations , composite-objective and implicit-update algorithms . In all cases , the results follow as simple corollaries within few lines of algebra .
Four different optimizers are used with the TF-CNN , Adagrad , ProximalAdagrad , Adam , and RMSProp to achieve accurate classification . The re-sult demonstrates that the loss value of the Adam and RMSProp optimizers was lower than the Adagrad and ProximalAdagrad optimizers . The classification accuracy using Adam optimizer is 95.8 % , while it reaches 100 % when using RMSProp optimizer .
In this paper , we propose an efficient parallel framework for translating embedding methods , called ParTrans-X , which enables the methods to be paralleled without locks by utilizing the distinguished structures of knowledge graphs . Experiments on two datasets with three typical translating embedding methods , i.e. , TransE [ 3 ] , TransH [ 19 ] , and a more efficient variant TransE- AdaGrad [ 11 ] validate that ParTrans-X can speed up the training process by more than an order of magnitude .
The O ( log T √ T ) nonasymptotic convergence rates of AdaHB and AdaNAG in non-convex stochastic setting are also jointly characterized by leveraging a newly developed unified formulation of these two momentum mechanisms . In particular , when momentum term vanishes we obtain convergence rate of coordinate-wise AdaGrad in non-convex stochastic setting as a byproduct .
Moreover , comparisons have been made between AdaHB , AdaNAG , Adam and RMSProp , which , to a certain extent , explains the reasons why Adam and RMSProp are divergent . In particular , when momentum term vanishes we obtain convergence rate of coordinate-wise AdaGrad in non-convex stochastic setting as a byproduct .
Additionally , each actor / learner keeps a running average and standard deviation of the absolute DQN loss for the data it sees and discards gradients with absolute loss higher than the mean plus several standard deviations . Finally , we used the AdaGrad update rule . section : Experiments
We repeat the above iterations until stopping . We adopt AdaGrad duchi2011adaptive to dynamically compute the learning rates for each iteration . Since the source and target tasks might have different convergence rates , we do early stopping on the target task performance .
λ is set as 0.001 based on the validation . Since the input is sparse , we use Adagrad [ reference ] for optimization . We repeat this evaluation 10 times and report mean accuracy .
Duality and equilibrium prices in economics of uncertainty A recourse certainty equivalent for decisions under uncertainty A stochastic approach for the optimization of open-loop engine control systems Smoothing Policies and Safe Policy Gradients Model Predictive Control-Based Battery Scheduling and Incentives to Manipulate Demand Response Baselines Market-Driven Energy Storage Planning for Microgrids with Renewable Energy Systems Using Stochastic Programming Energy Management for Multi-User Mobile-Edge Computing Systems with Energy Harvesting Devices and QoS Constraints Optimal operation of hybrid electrical and thermal energy storage systems under uncertain loading condition ECG-Gated Interventional Cardiac Reconstruction for Non-periodic Motion Robust Groupwise Affine Registration of Medical Images with Stochastic Optimization Multi-label Selective Ensemble Mode-independent control of singular Markovian jump systems: A stochastic optimization viewpoint An adaptive control momentum method as an optimizer in the cloud Recurrent Neural Network Grammars Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift Second-order Information in First-order Optimization Methods Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks Non-asymptotic Convergence of Adam-type Reinforcement Learning Algorithms under Markovian Sampling Variants of RMSProp and Adagrad with Logarithmic Regret Bounds Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets On stochastic optimization methods for Monte Carlo least-squares problems A unified modular analysis of online and stochastic optimization: adaptivity, optimism, non-convexity The Impact of Multi-Optimizers and Data Augmentation on TensorFlow Convolutional Neural Network Performance Efficient parallel translating embedding for knowledge graphs On the Convergence of AdaGrad with Momentum for Training Deep Neural Networks On the Convergence of Weighted AdaGrad with Momentum for Training Deep Neural Networks Massively Parallel Methods for Deep Reinforcement Learning Transfer Learning for Sequence Tagging with Hierarchical Recurrent Networks Asymmetric Tri-training for Unsupervised Domain Adaptation
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ICCCN MICCAI (1) Bildverarbeitung f&uuml;r die Medizin MCS HLT-NAACL ICML ICLR MIPR WI ArXiv ICLR ICML
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