arXiv subjects

Kamyar Azizzadenesheli

Publications and source records attributed to Kamyar Azizzadenesheli.

100 records · Page 6Linked to original sources

arXiv2019

Neural Lander: Stable Drone Landing Control using Learned Dynamics

Precise near-ground trajectory control is difficult for multi-rotor drones, due to the complex aerodynamic effects caused by interactions between multi-rotor airflow and the environment. Conventional control methods often fail to properly account for these complex effects and fall short in accomplishing smooth landing. In this paper, we present a novel deep-learning-based robust nonlinear controller (Neural Lander) that improves control performance of a quadrotor during landing. Our approach combines a nominal dynamics model with a Deep Neural Network (DNN) that learns high-order interactions. We apply spectral normalization (SN) to constrain the Lipschitz constant of the DNN. Leveraging this Lipschitz property, we design a nonlinear feedback linearization controller using the learned model and prove system stability with disturbance rejection. To the best of our knowledge, this is the first DNN-based nonlinear feedback controller with stability guarantees that can utilize arbitrarily large neural nets. Experimental results demonstrate that the proposed controller significantly outperforms a Baseline Nonlinear Tracking Controller in both landing and cross-table trajectory tracking cases. We also empirically show that the DNN generalizes well to unseen data outside the training domain.

cs.RO↗

arXiv2019

signSGD with Majority Vote is Communication Efficient And Fault Tolerant

Training neural networks on large datasets can be accelerated by distributing the workload over a network of machines. As datasets grow ever larger, networks of hundreds or thousands of machines become economically viable. The time cost of communicating gradients limits the effectiveness of using such large machine counts, as may the increased chance of network faults. We explore a particularly simple algorithm for robust, communication-efficient learning---signSGD. Workers transmit only the sign of their gradient vector to a server, and the overall update is decided by a majority vote. This algorithm uses $32\times$ less communication per iteration than full-precision, distributed SGD. Under natural conditions verified by experiment, we prove that signSGD converges in the large and mini-batch settings, establishing convergence for a parameter regime of Adam as a byproduct. Aggregating sign gradients by majority vote means that no individual worker has too much power. We prove that unlike SGD, majority vote is robust when up to 50% of workers behave adversarially. The class of adversaries we consider includes as special cases those that invert or randomise their gradient estimate. On the practical side, we built our distributed training system in Pytorch. Benchmarking against the state of the art collective communications library (NCCL), our framework---with the parameter server housed entirely on one machine---led to a 25% reduction in time for training resnet50 on Imagenet when using 15 AWS p3.2xlarge machines.

cs.DC↗

arXiv2019

Stochastic Linear Bandits with Hidden Low Rank Structure

High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures like sparsity are not valid anymore. Subspace recovery methods, such as Principle Component Analysis (PCA) can find the underlying low-rank structures in the feature space and reduce the complexity of the learning tasks. In this work, we propose Projected Stochastic Linear Bandit (PSLB), an algorithm for high dimensional stochastic linear bandits (SLB) when the representation of actions has an underlying low-dimensional subspace structure. PSLB deploys PCA based projection to iteratively find the low rank structure in SLBs. We show that deploying projection methods assures dimensionality reduction and results in a tighter regret upper bound that is in terms of the dimensionality of the subspace and its properties, rather than the dimensionality of the ambient space. We modify the image classification task into the SLB setting and empirically show that, when a pre-trained DNN provides the high dimensional feature representations, deploying PSLB results in significant reduction of regret and faster convergence to an accurate model compared to state-of-art algorithm.

cs.LG↗

arXiv2018

signSGD: Compressed Optimisation for Non-Convex Problems

Training large neural networks requires distributing learning across multiple workers, where the cost of communicating gradients can be a significant bottleneck. signSGD alleviates this problem by transmitting just the sign of each minibatch stochastic gradient. We prove that it can get the best of both worlds: compressed gradients and SGD-level convergence rate. The relative $\ell_1/\ell_2$ geometry of gradients, noise and curvature informs whether signSGD or SGD is theoretically better suited to a particular problem. On the practical side we find that the momentum counterpart of signSGD is able to match the accuracy and convergence speed of Adam on deep Imagenet models. We extend our theory to the distributed setting, where the parameter server uses majority vote to aggregate gradient signs from each worker enabling 1-bit compression of worker-server communication in both directions. Using a theorem by Gauss we prove that majority vote can achieve the same reduction in variance as full precision distributed SGD. Thus, there is great promise for sign-based optimisation schemes to achieve fast communication and fast convergence. Code to reproduce experiments is to be found at https://github.com/jxbz/signSGD .

cs.LG↗

arXiv2018

Reinforcement Learning in Rich-Observation MDPs using Spectral Methods

Reinforcement learning (RL) in Markov decision processes (MDPs) with large state spaces is a challenging problem. The performance of standard RL algorithms degrades drastically with the dimensionality of state space. However, in practice, these large MDPs typically incorporate a latent or hidden low-dimensional structure. In this paper, we study the setting of rich-observation Markov decision processes (ROMDP), where there are a small number of hidden states which possess an injective mapping to the observation states. In other words, every observation state is generated through a single hidden state, and this mapping is unknown a priori. We introduce a spectral decomposition method that consistently learns this mapping, and more importantly, achieves it with low regret. The estimated mapping is integrated into an optimistic RL algorithm (UCRL), which operates on the estimated hidden space. We derive finite-time regret bounds for our algorithm with a weak dependence on the dimensionality of the observed space. In fact, our algorithm asymptotically achieves the same average regret as the oracle UCRL algorithm, which has the knowledge of the mapping from hidden to observed spaces. Thus, we derive an efficient spectral RL algorithm for ROMDPs.

cs.AI↗

arXiv2018

Combating Reinforcement Learning's Sisyphean Curse with Intrinsic Fear

Many practical environments contain catastrophic states that an optimal agent would visit infrequently or never. Even on toy problems, Deep Reinforcement Learning (DRL) agents tend to periodically revisit these states upon forgetting their existence under a new policy. We introduce intrinsic fear (IF), a learned reward shaping that guards DRL agents against periodic catastrophes. IF agents possess a fear model trained to predict the probability of imminent catastrophe. This score is then used to penalize the Q-learning objective. Our theoretical analysis bounds the reduction in average return due to learning on the perturbed objective. We also prove robustness to classification errors. As a bonus, IF models tend to learn faster, owing to reward shaping. Experiments demonstrate that intrinsic-fear DQNs solve otherwise pathological environments and improve on several Atari games.

cs.LG↗

arXiv2018

Stochastic Activation Pruning for Robust Adversarial Defense

Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and cast the problem as a minimax zero-sum game between the adversary and the model. In general, for such games, the optimal strategy for both players requires a stochastic policy, also known as a mixed strategy. In this light, we propose Stochastic Activation Pruning (SAP), a mixed strategy for adversarial defense. SAP prunes a random subset of activations (preferentially pruning those with smaller magnitude) and scales up the survivors to compensate. We can apply SAP to pretrained networks, including adversarially trained models, without fine-tuning, providing robustness against adversarial examples. Experiments demonstrate that SAP confers robustness against attacks, increasing accuracy and preserving calibration.

cs.LG↗

arXiv2017

Experimental results : Reinforcement Learning of POMDPs using Spectral Methods

We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging since the learner interacts with the environment and possibly changes the future observations in the process. We devise a learning algorithm running through epochs, in each epoch we employ spectral techniques to learn the POMDP parameters from a trajectory generated by a fixed policy. At the end of the epoch, an optimization oracle returns the optimal memoryless planning policy which maximizes the expected reward based on the estimated POMDP model. We prove an order-optimal regret bound with respect to the optimal memoryless policy and efficient scaling with respect to the dimensionality of observation and action spaces.

cs.AI↗

arXiv2016

Open Problem: Approximate Planning of POMDPs in the class of Memoryless Policies

Planning plays an important role in the broad class of decision theory. Planning has drawn much attention in recent work in the robotics and sequential decision making areas. Recently, Reinforcement Learning (RL), as an agent-environment interaction problem, has brought further attention to planning methods. Generally in RL, one can assume a generative model, e.g. graphical models, for the environment, and then the task for the RL agent is to learn the model parameters and find the optimal strategy based on these learnt parameters. Based on environment behavior, the agent can assume various types of generative models, e.g. Multi Armed Bandit for a static environment, or Markov Decision Process (MDP) for a dynamic environment. The advantage of these popular models is their simplicity, which results in tractable methods of learning the parameters and finding the optimal policy. The drawback of these models is again their simplicity: these models usually underfit and underestimate the actual environment behavior. For example, in robotics, the agent usually has noisy observations of the environment inner state and MDP is not a suitable model. More complex models like Partially Observable Markov Decision Process (POMDP) can compensate for this drawback. Fitting this model to the environment, where the partial observation is given to the agent, generally gives dramatic performance improvement, sometimes unbounded improvement, compared to MDP. In general, finding the optimal policy for the POMDP model is computationally intractable and fully non convex, even for the class of memoryless policies. The open problem is to come up with a method to find an exact or an approximate optimal stochastic memoryless policy for POMDP models.

cs.AI↗

arXiv2016

Reinforcement Learning of POMDPs using Spectral Methods

We propose a new reinforcement learning algorithm for partially observable Markov decision processes (POMDP) based on spectral decomposition methods. While spectral methods have been previously employed for consistent learning of (passive) latent variable models such as hidden Markov models, POMDPs are more challenging since the learner interacts with the environment and possibly changes the future observations in the process. We devise a learning algorithm running through episodes, in each episode we employ spectral techniques to learn the POMDP parameters from a trajectory generated by a fixed policy. At the end of the episode, an optimization oracle returns the optimal memoryless planning policy which maximizes the expected reward based on the estimated POMDP model. We prove an order-optimal regret bound with respect to the optimal memoryless policy and efficient scaling with respect to the dimensionality of observation and action spaces.

cs.AI↗