Markov Models
What is Going on Inside Recurrent Meta Reinforcement Learning Agents?
Recurrent meta reinforcement learning (meta-RL) agents are agents that employ a recurrent neural network (RNN) for the purpose of "learning a learning algorithm". After being trained on a pre-specified task distribution, the learned weights of the agent's RNN are said to implement an efficient learning algorithm through their activity dynamics, which allows the agent to quickly solve new tasks sampled from the same distribution. However, due to the black-box nature of these agents, the way in which they work is not yet fully understood. In this study, we shed light on the internal working mechanisms of these agents by reformulating the meta-RL problem using the Partially Observable Markov Decision Process (POMDP) framework. We hypothesize that the learned activity dynamics is acting as belief states for such agents. Several illustrative experiments suggest that this hypothesis is true, and that recurrent meta-RL agents can be viewed as agents that learn to act optimally in partially observable environments consisting of multiple related tasks. This view helps in understanding their failure cases and some interesting model-based results reported in the literature.
Approximate Bayesian Computation for an Explicit-Duration Hidden Markov Model of COVID-19 Hospital Trajectories
Visani, Gian Marco, Lee, Alexandra Hope, Nguyen, Cuong, Kent, David M., Wong, John B., Cohen, Joshua T., Hughes, Michael C.
We address the problem of modeling constrained hospital resources in the midst of the COVID-19 pandemic in order to inform decision-makers of future demand and assess the societal value of possible interventions. For broad applicability, we focus on the common yet challenging scenario where patient-level data for a region of interest are not available. Instead, given daily admissions counts, we model aggregated counts of observed resource use, such as the number of patients in the general ward, in the intensive care unit, or on a ventilator. In order to explain how individual patient trajectories produce these counts, we propose an aggregate count explicit-duration hidden Markov model, nicknamed the ACED-HMM, with an interpretable, compact parameterization. We develop an Approximate Bayesian Computation approach that draws samples from the posterior distribution over the model's transition and duration parameters given aggregate counts from a specific location, thus adapting the model to a region or individual hospital site of interest. Samples from this posterior can then be used to produce future forecasts of any counts of interest. Using data from the United States and the United Kingdom, we show our mechanistic approach provides competitive probabilistic forecasts for the future even as the dynamics of the pandemic shift. Furthermore, we show how our model provides insight about recovery probabilities or length of stay distributions, and we suggest its potential to answer challenging what-if questions about the societal value of possible interventions.
Rule-based Shielding for Partially Observable Monte-Carlo Planning
Mazzi, Giulio, Castellini, Alberto, Farinelli, Alessandro
Partially Observable Monte-Carlo Planning (POMCP) is a powerful online algorithm able to generate approximate policies for large Partially Observable Markov Decision Processes. The online nature of this method supports scalability by avoiding complete policy representation. The lack of an explicit representation however hinders policy interpretability and makes policy verification very complex. In this work, we propose two contributions. The first is a method for identifying unexpected actions selected by POMCP with respect to expert prior knowledge of the task. The second is a shielding approach that prevents POMCP from selecting unexpected actions. The first method is based on Satisfiability Modulo Theory (SMT). It inspects traces (i.e., sequences of belief-action-observation triplets) generated by POMCP to compute the parameters of logical formulas about policy properties defined by the expert. The second contribution is a module that uses online the logical formulas to identify anomalous actions selected by POMCP and substitutes those actions with actions that satisfy the logical formulas fulfilling expert knowledge. We evaluate our approach on Tiger, a standard benchmark for POMDPs, and a real-world problem related to velocity regulation in mobile robot navigation. Results show that the shielded POMCP outperforms the standard POMCP in a case study in which a wrong parameter of POMCP makes it select wrong actions from time to time. Moreover, we show that the approach keeps good performance also if the parameters of the logical formula are optimized using trajectories containing some wrong actions.
Graph Decoupling Attention Markov Networks for Semi-supervised Graph Node Classification
Chen, Jie, Chen, Shouzhen, Bai, Mingyuan, Pu, Jian, Zhang, Junping, Gao, Junbin
Graph neural networks (GNN) have been ubiquitous in graph learning tasks such as node classification. Most of GNN methods update the node embedding iteratively by aggregating its neighbors' information. However, they often suffer from negative disturbance, due to edges connecting nodes with different labels. One approach to alleviate this negative disturbance is to use attention, but current attention always considers feature similarity and suffers from the lack of supervision. In this paper, we consider the label dependency of graph nodes and propose a decoupling attention mechanism to learn both hard and soft attention. The hard attention is learned on labels for a refined graph structure with fewer inter-class edges. Its purpose is to reduce the aggregation's negative disturbance. The soft attention is learned on features maximizing the information gain by message passing over better graph structures. Moreover, the learned attention guides the label propagation and the feature propagation. Extensive experiments are performed on five well-known benchmark graph datasets to verify the effectiveness of the proposed method.
Multi-resource allocation for federated settings: A non-homogeneous Markov chain model
Alam, Syed Eqbal, Wirth, Fabian, Yu, Jia Yuan
In a federated setting, agents coordinate with a central agent or a server to solve an optimization problem in which agents do not share their information with each other. Wirth and his co-authors, in a recent paper, describe how the basic additive-increase multiplicative-decrease (AIMD) algorithm can be modified in a straightforward manner to solve a class of optimization problems for federated settings for a single shared resource with no inter-agent communication. The AIMD algorithm is one of the most successful distributed resource allocation algorithms currently deployed in practice. It is best known as the backbone of the Internet and is also widely explored in other application areas. We extend the single-resource algorithm to multiple heterogeneous shared resources that emerge in smart cities, sharing economy, and many other applications. Our main results show the convergence of the average allocations to the optimal values. We model the system as a non-homogeneous Markov chain with place-dependent probabilities. Furthermore, simulation results are presented to demonstrate the efficacy of the algorithms and to highlight the main features of our analysis.
Financial Engineering and Artificial Intelligence in Python
Created by Lazy Programmer Team, Lazy Programmer Inc.Preview this Course - GET COUPON CODE Have you ever thought about what would happen if you combined the power of machine learning and artificial intelligence with financial engineering? Today, you can stop imagining, and start doing. This course will teach you the core fundamentals of financial engineering, with a machine learning twist. We will cover must-know topics in financial engineering, such as: Exploratory data analysis, significance testing, correlations, alpha and beta Time series analysis, simple moving average, exponentially-weighted moving average Holt-Winters exponential smoothing model Efficient Market Hypothesis Random Walk Hypothesis Time series forecasting ("stock price prediction") Modern portfolio theory Efficient frontier / Markowitz bullet Mean-variance optimization Maximizing the Sharpe ratio Convex optimization with Linear Programming and Quadratic Programming Capital Asset Pricing Model (CAPM) Algorithmic trading (VIP only) Statistical Factor Models (VIP only) Regime Detection with Hidden Markov Models (VIP only) In addition, we will look at various non-traditional techniques which stem purely from the field of machine learning and artificial intelligence, such as: Classification models Unsupervised learning Reinforcement learning and Q-learning ***VIP-only sections (get it while it lasts!) You will learn exactly why their methodology is fundamentally flawed and why their results are complete nonsense.
Deep Probabilistic Graphical Modeling
Probabilistic graphical modeling (PGM) provides a framework for formulating an interpretable generative process of data and expressing uncertainty about unknowns, but it lacks flexibility. Deep learning (DL) is an alternative framework for learning from data that has achieved great empirical success in recent years. DL offers great flexibility, but it lacks the interpretability and calibration of PGM. This thesis develops deep probabilistic graphical modeling (DPGM.) DPGM consists in leveraging DL to make PGM more flexible. DPGM brings about new methods for learning from data that exhibit the advantages of both PGM and DL. We use DL within PGM to build flexible models endowed with an interpretable latent structure. One model class we develop extends exponential family PCA using neural networks to improve predictive performance while enforcing the interpretability of the latent factors. Another model class we introduce enables accounting for long-term dependencies when modeling sequential data, which is a challenge when using purely DL or PGM approaches. Finally, DPGM successfully solves several outstanding problems of probabilistic topic models, a widely used family of models in PGM. DPGM also brings about new algorithms for learning with complex data. We develop reweighted expectation maximization, an algorithm that unifies several existing maximum likelihood-based algorithms for learning models parameterized by neural networks. This unifying view is made possible using expectation maximization, a canonical inference algorithm in PGM. We also develop entropy-regularized adversarial learning, a learning paradigm that deviates from the traditional maximum likelihood approach used in PGM. From the DL perspective, entropy-regularized adversarial learning provides a solution to the long-standing mode collapse problem of generative adversarial networks, a widely used DL approach.
Learning to reflect: A unifying approach for data-driven stochastic control strategies
Christensen, Sören, Strauch, Claudia, Trottner, Lukas
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their practicability suffers from the assumption of known dynamics of the underlying stochastic process, raising the statistical challenge of developing purely data-driven strategies. For the mathematically separated classes of continuous diffusion processes and L\'evy processes, we show that developing efficient strategies for related singular stochastic control problems can essentially be reduced to finding rate-optimal estimators with respect to the sup-norm risk of objects associated to the invariant distribution of ergodic processes which determine the theoretical solution of the control problem. From a statistical perspective, we exploit the exponential $\beta$-mixing property as the common factor of both scenarios to drive the convergence analysis, indicating that relying on general stability properties of Markov processes is a sufficiently powerful and flexible approach to treat complex applications requiring statistical methods. We show moreover that in the L\'evy case $-$ even though per se jump processes are more difficult to handle both in statistics and control theory $-$ a fully data-driven strategy with regret of significantly better order than in the diffusion case can be constructed.
DRL: Deep Reinforcement Learning for Intelligent Robot Control -- Concept, Literature, and Future
Combination of machine learning (for generating machine intelligence), computer vision (for better environment perception), and robotic systems (for controlled environment interaction) motivates this work toward proposing a vision-based learning framework for intelligent robot control as the ultimate goal (vision-based learning robot). This work specifically introduces deep reinforcement learning as the the learning framework, a General-purpose framework for AI (AGI) meaning application-independent and platform-independent. In terms of robot control, this framework is proposing specifically a high-level control architecture independent of the low-level control, meaning these two required level of control can be developed separately from each other. In this aspect, the high-level control creates the required intelligence for the control of the platform using the recorded low-level controlling data from that same platform generated by a trainer. The recorded low-level controlling data is simply indicating the successful and failed experiences or sequences of experiments conducted by a trainer using the same robotic platform. The sequences of the recorded data are composed of observation data (input sensor), generated reward (feedback value) and action data (output controller). For experimental platform and experiments, vision sensors are used for perception of the environment, different kinematic controllers create the required motion commands based on the platform application, deep learning approaches generate the required intelligence, and finally reinforcement learning techniques incrementally improve the generated intelligence until the mission is accomplished by the robot.
CVLight: Deep Reinforcement Learning for Adaptive Traffic Signal Control with Connected Vehicles
Li, Wangzhi, Cai, Yaxing, Dinesha, Ujwal, Fu, Yongjie, Di, Xuan
This paper develops a reinforcement learning (RL) scheme for adaptive traffic signal control (ATSC), called "CVLight", that leverages data collected only from connected vehicles (CV). Seven types of RL models are proposed within this scheme that contain various state and reward representations, including incorporation of CV delay and green light duration into state and the usage of CV delay as reward. To further incorporate information of both CV and non-CV into CVLight, an algorithm based on actor-critic, A2C-Full, is proposed where both CV and non-CV information is used to train the critic network, while only CV information is used to update the policy network and execute optimal signal timing. These models are compared at an isolated intersection under various CV market penetration rates. A full model with the best performance (i.e., minimum average travel delay per vehicle) is then selected and applied to compare with state-of-the-art benchmarks under different levels of traffic demands, turning proportions, and dynamic traffic demands, respectively. Two case studies are performed on an isolated intersection and a corridor with three consecutive intersections located in Manhattan, New York, to further demonstrate the effectiveness of the proposed algorithm under real-world scenarios. Compared to other baseline models that use all vehicle information, the trained CVLight agent can efficiently control multiple intersections solely based on CV data and can achieve a similar or even greater performance when the CV penetration rate is no less than 20%.