Non-intrusive load monitoring (NILM) or energy disaggregation is an inverse problem whereby the goal is to extract the load profiles of individual appliances, given an aggregate load profile of the mains of a home. NILM could help identify the power usage patterns of individual appliances in a home, and thus, could help realize novel energy conservation schemes for smart homes. In this backdrop, this work proposes a novel deep-learning approach to solve the NILM problem and a few related problems as follows. 1) We build upon the reputed seq2-point convolutional neural network (CNN) model to come up with the proposed seq2-[3]-point CNN model to solve the (home) NILM problem and site-NILM problem (basically, NILM at a smaller scale). 2) We solve the related problem of appliance identification by building upon the state-of-the-art (pre-trained) 2D-CNN models, i.e., AlexNet, ResNet-18, and DenseNet-121, which are trained upon two custom datasets that consist of Wavelets and short-time Fourier transform (STFT)-based 2D electrical signatures of the appliances. 3) Finally, we do some basic qualitative inference about an individual appliance's health by comparing the power consumption of the same appliance across multiple homes. Low-frequency REDD dataset is used to train and test the proposed deep learning models for all problems, except site-NILM where REFIT dataset has been used. As for the results, we achieve a maximum accuracy of 94.6\% for home-NILM, 81\% for site-NILM, and 88.9\% for appliance identification (with Resnet-based model).

Given $X_1,\cdot ,X_N$ random variables whose joint distribution is given as $\mu$ we will use the Martingale Method to show any Lipshitz Function $f$ over these random variables is subgaussian. The Variance parameter however can have a simple expression under certain conditions. For example under the assumption that the random variables follow a Markov Chain and that the function is Lipschitz under a Weighted Hamming Metric. We shall conclude with certain well known techniques from concentration of suprema of random processes with applications in Reinforcement Learning

We study the constrained reinforcement learning problem, in which an agent aims to maximize the expected cumulative reward subject to a constraint on the expected total value of a utility function. In contrast to existing model-based approaches or model-free methods accompanied with a `simulator', we aim to develop the first model-free, simulator-free algorithm that achieves a sublinear regret and a sublinear constraint violation even in large-scale systems. To this end, we consider the episodic constrained Markov decision processes with linear function approximation, where the transition dynamics and the reward function can be represented as a linear function of some known feature mapping. We show that $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ regret and $\tilde{\mathcal{O}}(\sqrt{d^3H^3T})$ constraint violation bounds can be achieved, where $d$ is the dimension of the feature mapping, $H$ is the length of the episode, and $T$ is the total number of steps. Our bounds are attained without explicitly estimating the unknown transition model or requiring a simulator, and they depend on the state space only through the dimension of the feature mapping. Hence our bounds hold even when the number of states goes to infinity. Our main results are achieved via novel adaptations of the standard LSVI-UCB algorithms. In particular, we first introduce primal-dual optimization into the LSVI-UCB algorithm to balance between regret and constraint violation. More importantly, we replace the standard greedy selection with respect to the state-action function in LSVI-UCB with a soft-max policy. This turns out to be key in establishing uniform concentration for the constrained case via its approximation-smoothness trade-off. We also show that one can achieve an even zero constraint violation while still maintaining the same order with respect to $T$.

To integrate high amounts of renewable energy resources, electrical power grids must be able to cope with high amplitude, fast timescale variations in power generation. Frequency regulation through demand response has the potential to coordinate temporally flexible loads, such as air conditioners, to counteract these variations. Existing approaches for discrete control with dynamic constraints struggle to provide satisfactory performance for fast timescale action selection with hundreds of agents. We propose a decentralized agent trained with multi-agent proximal policy optimization with localized communication. We explore two communication frameworks: hand-engineered, or learned through targeted multi-agent communication. The resulting policies perform well and robustly for frequency regulation, and scale seamlessly to arbitrary numbers of houses for constant processing times.

We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local, i.e., a one time-step robust optimization problem leads to an optimizer of the global (i.e. infinite time-steps) robust stochastic optimal control problem, as well as to a corresponding worst-case measure. Moreover, we apply this framework to portfolio optimization involving data of the S&P 500. We present two different types of ambiguity sets; one is fully data-driven given by a Wasserstein-ball around the empirical measure, the second one is described by a parametric set of multivariate normal distributions, where the corresponding uncertainty sets of the parameters are estimated from the data. It turns out that in scenarios where the market is volatile or bearish, the optimal portfolio strategies from the corresponding robust optimization problem outperforms the ones without model uncertainty, showcasing the importance of taking model uncertainty into account.

We present a novel $Q$-learning algorithm to solve distributionally robust Markov decision problems, where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball around a (possibly estimated) reference measure. We prove convergence of the presented algorithm and provide several examples also using real data to illustrate both the tractability of our algorithm as well as the benefits of considering distributional robustness when solving stochastic optimal control problems, in particular when the estimated distributions turn out to be misspecified in practice.

Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying distributions are known and/or Gaussian. In practice, however, these assumptions may be unrealistic and can lead to poor approximations of the true noise distribution. We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions. In particular, we address the problem of computing a controller that provides probabilistic guarantees on safely reaching a target, while also avoiding unsafe regions of the state space. First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states. As a key contribution, we adapt tools from the scenario approach to compute probably approximately correct (PAC) bounds on these transition probabilities, based on a finite number of samples of the noise. We capture these bounds in the transition probability intervals of a so-called interval Markov decision process (iMDP). This iMDP is, with a user-specified confidence probability, robust against uncertainty in the transition probabilities, and the tightness of the probability intervals can be controlled through the number of samples. We use state-of-the-art verification techniques to provide guarantees on the iMDP and compute a controller for which these guarantees carry over to the original control system. In addition, we develop a tailored computational scheme that reduces the complexity of the synthesis of these guarantees on the iMDP. Benchmarks on realistic control systems show the practical applicability of our method, even when the iMDP has hundreds of millions of transitions.

We study the behavior of an economic platform (e.g., Amazon, Uber Eats, Instacart) under shocks, such as COVID-19 lockdowns, and the effect of different regulation considerations imposed on a platform. To this end, we develop a multi-agent Gym environment of a platform economy in a dynamic, multi-period setting, with the possible occurrence of economic shocks. Buyers and sellers are modeled as economically-motivated agents, choosing whether or not to pay corresponding fees to use the platform. We formulate the platform's problem as a partially observable Markov decision process, and use deep reinforcement learning to model its fee setting and matching behavior. We consider two major types of regulation frameworks: (1) taxation policies and (2) platform fee restrictions, and offer extensive simulated experiments to characterize regulatory tradeoffs under optimal platform responses. Our results show that while many interventions are ineffective with a sophisticated platform actor, we identify a particular kind of regulation -- fixing fees to optimal, pre-shock fees while still allowing a platform to choose how to match buyer demands to sellers -- as promoting the efficiency, seller diversity, and resilience of the overall economic system.

WQMIX, QMIX, QTRAN, and VDN are SOTA algorithms for Dec-POMDP. All of them cannot solve complex agents' cooperation domains. We give an algorithm to solve such problems. In the first stage, we solve a single-agent problem and get a policy. In the second stage, we solve the multi-agent problem with the single-agent policy. SA2MA has a clear advantage over all competitors in complex agents' cooperative domains.

In this study, we predict next-day movements of stock end-of-day implied volatility using random forests. Through an ablation study, we examine the usefulness of different sources of predictors and expose the value of attention and sentiment features extracted from Twitter. We study the approach on a stock universe comprised of the 165 most liquid US stocks diversified across the 11 traditional market sectors using a sizeable out-of-sample period spanning over six years. In doing so, we uncover that stocks in certain sectors, such as Consumer Discretionary, Technology, Real Estate, and Utilities are easier to predict than others. Further analysis shows that possible reasons for these discrepancies might be caused by either excess social media attention or low option liquidity. Lastly, we explore how our proposed approach fares throughout time by identifying four underlying market regimes in implied volatility using hidden Markov models. We find that most added value is achieved in regimes associated with lower implied volatility, but optimal regimes vary per market sector.