The power grid is a complex and vital system that necessitates careful reliability management. Managing the grid is a difficult problem with multiple time scales of decision making and stochastic behavior due to renewable energy generations, variable demand and unplanned outages. Solving this problem in the face of uncertainty requires a new methodology with tractable algorithms. In this work, we introduce a new model for hierarchical decision making in complex systems. We apply reinforcement learning (RL) methods to learn a proxy, i.e., a level of abstraction, for real-time power grid reliability. We devise an algorithm that alternates between slow time-scale policy improvement, and fast time-scale value function approximation. We compare our results to prevailing heuristics, and show the strength of our method.
For our proxy abstraction devise a hierarchical model. Hierarchical models, offer several benefits over flat models when appropriate. They can improve exploration, enable learning from fewer trials, and allow faster learning for new problems by reusing subtasks learned on previous problems @cite_29 . Standard approaches for hierarchical models include: planning with options (often referred to as skills) @cite_30 , task hierarchy @cite_17 and hierarchy of abstract machines @cite_9 . These models include levels of decision making that share the same state-space and a termination condition to switch between controllers. This structure does not fit our problem well where two separate decision makers run on state-spaces and resolutions.
@cite_30 @cite_9 @cite_29 @cite_17
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Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning. One popular approach for addressing this challenge is the options framework (, 2000). However, only recently in (, 2017) was a policy gradient theorem derived for online learning of general purpose options in an end to end fashion. In this work, we extend previous work on this topic that only focuses on learning a two-level hierarchy including options and primitive actions to enable learning simultaneously at multiple resolutions in time. We achieve this by considering an arbitrarily deep hierarchy of options where high level temporally extended options are composed of lower level options with finer resolutions in time. We extend results from (, 2017) and derive policy gradient theorems for a deep hierarchy of options. Our proposed hierarchical option-critic architecture is capable of learning internal policies, termination conditions, and hierarchical compositions over options without the need for any intrinsic rewards or subgoals. Our empirical results in both discrete and continuous environments demonstrate the efficiency of our framework. In this work, we take a representation learning perspective on hierarchical reinforcement learning, where the problem of learning lower layers in a hierarchy is transformed into the problem of learning trajectory-level generative models. We show that we can learn continuous latent representations of trajectories, which are effective in solving temporally extended and multi-stage problems. Our proposed model, SeCTAR, draws inspiration from variational autoencoders, and learns latent representations of trajectories. A key component of this method is to learn both a latent-conditioned policy and a latent-conditioned model which are consistent with each other. Given the same latent, the policy generates a trajectory which should match the trajectory predicted by the model. This model provides a built-in prediction mechanism, by predicting the outcome of closed loop policy behavior. We propose a novel algorithm for performing hierarchical RL with this model, combining model-based planning in the learned latent space with an unsupervised exploration objective. We show that our model is effective at reasoning over long horizons with sparse rewards for several simulated tasks, outperforming standard reinforcement learning methods and prior methods for hierarchical reasoning, model-based planning, and exploration. This dissertation presents a hierarchical controller which can learn to perform complex motor skills. Humans routinely coordinate many degrees of freedom smoothly and effortlessly to achieve complex goals. Moreover, we are good at learning new patterns of coordination to produce new skills. Robots and artificial systems, on the other hand, typically have difficulty with the kinds of behaviors that come most naturally to us. Skills such as running, skiing, playing basketball, or diving involve complex nonlinear dynamics, many degrees of freedom, and behavioral goals that can be difficult to specify mathematically; goals such as “ski down the mountain without falling down” or “shoot a layup” must be translated from linguistic requirements into dynamic system constraints. The focus in this dissertation will be on the skill of platform diving, in which the diver's goal is to execute a certain dive and enter the water in a fully-extended, vertical position. Controlling a simulated diver is a difficult problem for standard control and planning algorithms; conservation of angular momentum gives the system dynamics a nonholonomic constraint with nonlinear drift. In this dissertation, ideas from the fields of biological motor control and learning are combined with new learning algorithms in the design of a hierarchical controller which learns to dive. At the lower level of the control hierarchy, each degree of freedom in the diver's joints is assigned a controller based on biological pattern generators for fast, single-joint movements. These controllers contain neural networks, which are trained on data generated by simulation. The higher level of the control hierarchy incorporates ideas from human skill learning: to achieve a desired behavior pattern, a human learning a new skill uses information from instructors and from watching other performers to build a mental model of the task requirements, and then practices to refine the parameters of this behavioral model. In the high-level controller, each dive is represented as a sequence of multi-joint synergies. The controller learns initial estimates of the timing of these synergies from observational data and then refines these estimates through Q-learning with repeated simulations. Safe state abstraction in reinforcement learning allows an agent to ignore aspects of its current state that are irrelevant to its current decision, and therefore speeds up dynamic programming and learning. This paper explores safe state abstraction in hierarchical reinforcement learning, where learned behaviors must conform to a given partial, hierarchical program. Unlike previous approaches to this problem, our methods yield significant state abstraction while maintaining hierarchical optimality, i.e., optimality among all policies consistent with the partial program. We show how to achieve this for a partial programming language that is essentially Lisp augmented with nondeterministic constructs. We demonstrate our methods on two variants of Dietterich's taxi domain, showing how state abstraction and hierarchical optimality result in faster learning of better policies and enable the transfer of learned skills from one problem to another. In this work we propose a hierarchical approach for labeling semantic objects and regions in scenes. Our approach is reminiscent of early vision literature in that we use a decomposition of the image in order to encode relational and spatial information. In contrast to much existing work on structured prediction for scene understanding, we bypass a global probabilistic model and instead directly train a hierarchical inference procedure inspired by the message passing mechanics of some approximate inference procedures in graphical models. This approach mitigates both the theoretical and empirical difficulties of learning probabilistic models when exact inference is intractable. In particular, we draw from recent work in machine learning and break the complex inference process into a hierarchical series of simple machine learning subproblems. Each subproblem in the hierarchy is designed to capture the image and contextual statistics in the scene. This hierarchy spans coarse-to-fine regions and explicitly models the mixtures of semantic labels that may be present due to imperfect segmentation. To avoid cascading of errors and overfitting, we train the learning problems in sequence to ensure robustness to likely errors earlier in the inference sequence and leverage the stacking approach developed by Hierarchical feature learning based on convolutional neural networks (CNN) has recently shown significant potential in various computer vision tasks. While allowing high-quality discriminative feature learning, the downside of CNNs is the lack of explicit structure in features, which often leads to overfitting, absence of reconstruction from partial observations and limited generative abilities. Explicit structure is inherent in hierarchical compositional models, however, these lack the ability to optimize a well-defined cost function. We propose a novel analytic model of a basic unit in a layered hierarchical model with both explicit compositional structure and a well-defined discriminative cost function. Our experiments on two datasets show that the proposed compositional model performs on a par with standard CNNs on discriminative tasks, while, due to explicit modeling of the structure in the feature units, affording a straight-forward visualization of parts and faster inference due to separability of the units. Actions We study the problem of representation learning in goal-conditioned hierarchical reinforcement learning. In such hierarchical structures, a higher-level controller solves tasks by iteratively communicating goals which a lower-level policy is trained to reach. Accordingly, the choice of representation -- the mapping of observation space to goal space -- is crucial. To study this problem, we develop a notion of sub-optimality of a representation, defined in terms of expected reward of the optimal hierarchical policy using this representation. We derive expressions which bound the sub-optimality and show how these expressions can be translated to representation learning objectives which may be optimized in practice. Results on a number of difficult continuous-control tasks show that our approach to representation learning yields qualitatively better representations as well as quantitatively better hierarchical policies, compared to existing methods (see videos at this https URL). Learning, planning, and representing knowledge at multiple levels of temporal ab- straction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforce- ment learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options—closed-loop policies for taking ac- tion over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as mus- cle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning frame- work in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic pro- gramming and in learning methods such as Q-learning. Formally, a set of options defined over an MDP constitutes a semi-Markov decision process (SMDP), and the theory of SMDPs provides the foundation for the theory of options. However, the most interesting issues concern the interplay between the underlying MDP and the SMDP and are thus beyond SMDP theory. We present results for three such cases: 1) we show that the results of planning with options can be used during execution to interrupt options and thereby perform even better than planned, 2) we introduce new intra-option methods that are able to learn about an option from fragments of its execution, and 3) we propose a notion of subgoal that can be used to improve the options themselves. All of these results have precursors in the existing literature; the contribution of this paper is to establish them in a simpler and more general setting with fewer changes to the existing reinforcement learning framework. In particular, we show that these results can be obtained without committing to (or ruling out) any particular approach to state abstraction, hierarchy, function approximation, or the macro-utility problem. We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex learning tasks that benefit from iterative inference and temporal modeling. The architecture shows close-to-optimal results on temporal modeling of video data, competitive results on music modeling, and improved perceptual grouping based on higher order abstractions, such as stochastic textures and motion cues. We present results for fully supervised, semi-supervised, and unsupervised tasks. The results suggest that the proposed architecture and principles are powerful tools for learning a hierarchy of abstractions, learning iterative inference and handling temporal information. We propose a recurrent extension of the Ladder networks whose structure is motivated by the inference required in hierarchical latent variable models. We demonstrate that the recurrent Ladder is able to handle a wide variety of complex learning tasks that benefit from iterative inference and temporal modeling. The architecture shows close-to-optimal results on temporal modeling of video data, competitive results on music modeling, and improved perceptual grouping based on higher order abstractions, such as stochastic textures and motion cues. We present results for fully supervised, semi-supervised, and unsupervised tasks. The results suggest that the proposed architecture and principles are powerful tools for learning a hierarchy of abstractions, learning iterative inference and handling temporal information. This paper presents a new approach to hierarchical reinforcement learning based on decomposing the target Markov decision process (MDP) into a hierarchy of smaller MDPs and decomposing the value function of the target MDP into an additive combination of the value functions of the smaller MDPs. The decomposition, known as the MAXQ decomposition, has both a procedural semantics--as a subroutine hierarchy--and a declarative semantics--as a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. It is based on the assumption that the programmer can identify useful subgoals and define subtasks that achieve these subgoals. By defining such subgoals, the programmer constrains the set of policies that need to be considered during reinforcement learning. The MAXQ value function decomposition can represent the value function of any policy that is consistent with the given hierarchy. The decomposition also creates opportunities to exploit state abstractions, so that individual MDPs within the hierarchy can ignore large parts of the state space. This is important for the practical application of the method. This paper defines the MAXQ hierarchy, proves formal results on its representational power, and establishes five conditions for the safe use of state abstractions. The paper presents an online model-free learning algorithm, MAXQ-Q, and proves that it converges with probability 1 to a kind of locally-optimal policy known as a recursively optimal policy, even in the presence of the five kinds of state abstraction. The paper evaluates the MAXQ representation and MAXQ-Q through a series of experiments in three domains and shows experimentally that MAXQ-Q (with state abstractions) converges to a recursively optimal policy much faster than flat Q learning. The fact that MAXQ learns a representation of the value function has an important benefit: it makes it possible to compute and execute an improved, non-hierarchical policy via a procedure similar to the policy improvement step of policy iteration. The paper demonstrates the effectiveness of this nonhierarchical execution experimentally. Finally, the paper concludes with a comparison to related work and a discussion of the design tradeoffs in hierarchical reinforcement learning. We propose a novel unsupervised learning framework to model activities and interactions in crowded and complicated scenes. Hierarchical Bayesian models are used to connect three elements in visual surveillance: low-level visual features, simple "atomic" activities, and interactions. Atomic activities are modeled as distributions over low-level visual features, and multi-agent interactions are modeled as distributions over atomic activities. These models are learnt in an unsupervised way. Given a long video sequence, moving pixels are clustered into different atomic activities and short video clips are clustered into different interactions. In this paper, we propose three hierarchical Bayesian models, Latent Dirichlet Allocation (LDA) mixture model, Hierarchical Dirichlet Process (HDP) mixture model, and Dual Hierarchical Dirichlet Processes (Dual-HDP) model. They advance existing language models, such as LDA [1] and HDP [2]. Our data sets are challenging video sequences from crowded traffic scenes and train station scenes with many kinds of activities co-occurring. Without tracking and human labeling effort, our framework completes many challenging visual surveillance tasks of board interest such as: (1) discovering typical atomic activities and interactions; (2) segmenting long video sequences into different interactions; (3) segmenting motions into different activities; (4) detecting abnormality; and (5) supporting high-level queries on activities and interactions. Recent progress has shown that learning from hierarchical feature representations leads to improvements in various computer vision tasks. Motivated by the observation that human activity data contains information at various temporal resolutions, we present a hierarchical sequence summarization approach for action recognition that learns multiple layers of discriminative feature representations at different temporal granularities. We build up a hierarchy dynamically and recursively by alternating sequence learning and sequence summarization. For sequence learning we use CRFs with latent variables to learn hidden spatio-temporal dynamics, for sequence summarization we group observations that have similar semantic meaning in the latent space. For each layer we learn an abstract feature representation through non-linear gate functions. This procedure is repeated to obtain a hierarchical sequence summary representation. We develop an efficient learning method to train our model and show that its complexity grows sub linearly with the size of the hierarchy. Experimental results show the effectiveness of our approach, achieving the best published results on the Arm Gesture and Canal9 datasets. We address the problem of learning topic hierarchies from data. The model selection problem in this domain is daunting—which of the large collection of possible trees to use? We take a Bayesian approach, generating an appropriate prior via a distribution on partitions that we refer to as the nested Chinese restaurant process. This nonparametric prior allows arbitrarily large branching factors and readily accommodates growing data collections. We build a hierarchical topic model by combining this prior with a likelihood that is based on a hierarchical variant of latent Dirichlet allocation. We illustrate our approach on simulated data and with an application to the modeling of NIPS abstracts. Abstraction and hierarchical information-processing are hallmarks of human and animal intelligence underlying the unrivaled flexibility of behavior in biological systems. Achieving such a flexibility in artificial systems is challenging, even with more and more computational power. Here we investigate the hypothesis that abstraction and hierarchical information-processing might in fact be the consequence of limitations in information-processing power. In particular, we study an information-theoretic framework of bounded rational decision-making that trades off utility maximization against information-processing costs. We apply the basic principle of this framework to perception-action systems with multiple information-processing nodes and derive bounded optimal solutions. We show how the formation of abstractions and decision-making hierarchies depends on information-processing costs. We illustrate the theoretical ideas with example simulations and conclude by formalizing a mathematically unifying optimization principle that could potentially be extended to more complex systems. Abstract A problem domain can be represented as a hierarchy of abstraction spaces in which successively finer levels of detail are introduced. The problem solver ABSTRIPS, a modification of STRIPS, can define an abstraction space hierarchy from the STRIPS representation of a problem domain, and it can utilize the hierarchy in solving problems. Examples of the system's performance are presented that demonstrate the significant increases in problem-solving power that this approach provides. Then some further implications of the hierarchical planning approach are explored. In the pursuit of increasingly intelligent learning systems, abstraction plays a vital role in enabling sophisticated decisions to be made in complex environments. The options framework provides formalism for such abstraction over sequences of decisions. However most models require that options be given a priori, presumably specified by hand, which is neither efficient, nor scalable. Indeed, it is preferable to learn options directly from interaction with the environment. Despite several efforts, this remains a difficult problem: many approaches require access to a model of the environmental dynamics, and inferred options are often not interpretable, which limits our ability to explain the system behavior for verification or debugging purposes. In this work we develop a novel policy gradient method for the automatic learning of policies with options. This algorithm uses inference methods to simultaneously improve all of the options available to an agent, and thus can be employed in an off-policy manner, without observing option labels. Experimental results show that the options learned can be interpreted. Further, we find that the method presented here is more sample efficient than existing methods, leading to faster and more stable learning of policies with options. Decision making usually involves choosing among different courses of action over a broad range of time scales. For instance, a person planning a trip to a distant location makes high-level decisions regarding what means of transportation to use, but also chooses low-level actions, such as the movements for getting into a car. The problem of picking an appropriate time scale for reasoning and learning has been explored in artificial intelligence, control theory and robotics. In this dissertation we develop a framework that allows novel solutions to this problem, in the context of Markov Decision Processes (MDPs) and reinforcement learning. In this dissertation, we present a general framework for prediction, control and learning at multiple temporal scales. In this framework, temporally extended actions are represented by a way of behaving (a policy) together with a termination condition. An action represented in this way is called an option. Options can be easily incorporated in MDPs, allowing an agent to use existing controllers, heuristics for picking actions, or learned courses of action. The effects of behaving according to an option can be predicted using multi-time models, learned by interacting with the environment. In this dissertation we develop multi-time models, and we illustrate the way in which they can be used to produce plans of behavior very quickly, using classical dynamic programming or reinforcement learning techniques. The most interesting feature of our framework is that it allows an agent to work simultaneously with high-level and low-level temporal representations. The interplay of these levels can be exploited in order to learn and plan more efficiently and more accurately. We develop new algorithms that take advantage of this structure to improve the quality of plans, and to learn in parallel about the effects of many different options. In recent years, variants of a neural network architecture for statistical language modeling have been proposed and successfully applied, e.g. in the language modeling component of speech recognizers. The main advantage of these architectures is that they learn an embedding for words (or other symbols) in a continuous space that helps to smooth the language model and provide good generalization even when the number of training examples is insufficient. However, these models are extremely slow in comparison to the more commonly used n-gram models, both for training and recognition. As an alternative to an importance sampling method proposed to speed-up training, we introduce a hierarchical decomposition of the conditional probabilities that yields a speed-up of about 200 both during training and recognition. The hierarchical decomposition is a binary hierarchical clustering constrained by the prior knowledge extracted from the WordNet semantic hierarchy. Knowledge-based planning methods offer benefits over classical techniques, but they are time consuming and costly to construct. There has been research on learning plan knowledge from search, but this can take substantial computer time and may even fail to find solutions on complex tasks. Here we describe another approach that observes sequences of operators taken from expert solutions to problems and learns hierarchical task networks from them. The method has similarities to previous algorithms for explanation-based learning, but differs in its ability to acquire hierarchical structures and in the generality of learned conditions. These increase the method's capability to transfer learned knowledge to other problems and supports the acquisition of recursive procedures. After presenting the learning algorithm, we report experiments that compare its abilities to other techniques on two planning domains. In closing, we review related work and directions for future research.