We study convex Constrained Markov Decision Processes (CMDPs) in which the objective is concave and the constraints are convex in the state-action occupancy measure. We propose a policy-based primal-dual algorithm that updates the primal variable via policy gradient ascent and updates the dual variable via projected sub-gradient descent. Despite the loss of additivity structure and the nonconvex nature, we establish the global convergence of the proposed algorithm by leveraging a hidden convexity in the problem, and prove the $\mathcal{O}\left(T^{-1/3}\right)$ convergence rate in terms of both optimality gap and constraint violation. When the objective is strongly concave in the occupancy measure, we prove an improved convergence rate of $\mathcal{O}\left(T^{-1/2}\right)$. By introducing a pessimistic term to the constraint, we further show that a zero constraint violation can be achieved while preserving the same convergence rate for the optimality gap. This work is the first one in the literature that establishes non-asymptotic convergence guarantees for policy-based primal-dual methods for solving infinite-horizon discounted convex CMDPs.

Computational models starting from large ensembles of evolutionarily related protein sequences capture a representation of protein families and learn constraints associated to protein structure and function. They thus open the possibility for generating novel sequences belonging to protein families. Protein language models trained on multiple sequence alignments, such as MSA Transformer, are highly attractive candidates to this end. We propose and test an iterative method that directly employs the masked language modeling objective to generate sequences using MSA Transformer. We demonstrate that the resulting sequences score as well as natural sequences, for homology, coevolution and structure-based measures. For large protein families, our synthetic sequences have similar or better properties compared to sequences generated by Potts models, including experimentally-validated ones. Moreover, for small protein families, our generation method based on MSA Transformer outperforms Potts models. Our method also more accurately reproduces the higher-order statistics and the distribution of sequences in sequence space of natural data than Potts models. MSA Transformer is thus a strong candidate for protein sequence generation and protein design.

Active learning theories and methods have been extensively studied in classical statistical learning settings. However, deep active learning, i.e., active learning with deep learning models, is usually based on empirical criteria without solid theoretical justification, thus suffering from heavy doubts when some of those fail to provide benefits in real applications. In this paper, by exploring the connection between the generalization performance and the training dynamics, we propose a theory-driven deep active learning method (dynamicAL) which selects samples to maximize training dynamics. In particular, we prove that the convergence speed of training and the generalization performance are positively correlated under the ultra-wide condition and show that maximizing the training dynamics leads to better generalization performance. Furthermore, to scale up to large deep neural networks and data sets, we introduce two relaxations for the subset selection problem and reduce the time complexity from polynomial to constant. Empirical results show that dynamicAL not only outperforms the other baselines consistently but also scales well on large deep learning models. We hope our work would inspire more attempts on bridging the theoretical findings of deep networks and practical impacts of deep active learning in real applications.

Linear regression is a simple machine learning model and chances are you are already aware of it! Do you remember plotting the line y mx c in your introductory algebra class? This is an equation of a straight line where m is its gradient and c is the point where the line crosses the y-axis. Using this equation, you're able to estimate the value of y for any given value of x. Similarly, linear regression involves estimating the relationship between independent variables (x) and a dependent variable(y).

Markov Chain Monte Carlo (MCMC) methods are the workhorse of Bayesian computation when closed formulas for estimators or probability distributions are not available. For this reason they have been central to the development and success of high-dimensional Bayesian statistics in the last decades, where one attempts to generate samples from some posterior distribution Π( |data) arising from a prior Π on D-dimensional Euclidean space and the observed data vector. MCMC methods tend to perform well in a large variety of problems, are very flexible and user-friendly, and enjoy many theoretical guarantees. Under mild assumptions, they are known to converge to their stationary'target' distributions as a consequence of the ergodic theorem, albeit perhaps at a slow speed, requiring a large number of iterations to provide numerically accurate algorithms. When the target distribution is log-concave, MCMC algorithms are known to mix rapidly, even in high dimensions.

Nowadays, machine learning models and applications have become increasingly pervasive. With this rapid increase in the development and employment of machine learning models, a concern regarding privacy has risen. Thus, there is a legitimate need to protect the data from leaking and from any attacks. One of the strongest and most prevalent privacy models that can be used to protect machine learning models from any attacks and vulnerabilities is differential privacy (DP). DP is strict and rigid definition of privacy, where it can guarantee that an adversary is not capable to reliably predict if a specific participant is included in the dataset or not. It works by injecting a noise to the data whether to the inputs, the outputs, the ground truth labels, the objective functions, or even to the gradients to alleviate the privacy issue and protect the data. To this end, this survey paper presents different differentially private machine learning algorithms categorized into two main categories (traditional machine learning models vs. deep learning models). Moreover, future research directions for differential privacy with machine learning algorithms are outlined.

Gaining the trust of customers and providing them empathy are very critical in the financial domain. Frequent occurrence of fraudulent activities affects these two factors. Hence, financial organizations and banks must take utmost care to mitigate them. Among them, ATM fraudulent transaction is a common problem faced by banks. There following are the critical challenges involved in fraud datasets: the dataset is highly imbalanced, the fraud pattern is changing, etc. Owing to the rarity of fraudulent activities, Fraud detection can be formulated as either a binary classification problem or One class classification (OCC). In this study, we handled these techniques on an ATM transactions dataset collected from India. In binary classification, we investigated the effectiveness of various over-sampling techniques, such as the Synthetic Minority Oversampling Technique (SMOTE) and its variants, Generative Adversarial Networks (GAN), to achieve oversampling. Further, we employed various machine learning techniques viz., Naive Bayes (NB), Logistic Regression (LR), Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF), Gradient Boosting Tree (GBT), Multi-layer perceptron (MLP). GBT outperformed the rest of the models by achieving 0.963 AUC, and DT stands second with 0.958 AUC. DT is the winner if the complexity and interpretability aspects are considered. Among all the oversampling approaches, SMOTE and its variants were observed to perform better. In OCC, IForest attained 0.959 CR, and OCSVM secured second place with 0.947 CR. Further, we incorporated explainable artificial intelligence (XAI) and causal inference (CI) in the fraud detection framework and studied it through various analyses.

We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary arbitrarily over time with a budget on their cumulative variations. When this variation budget is known a prior, we propose two restart-based algorithms, namely Restart-RSMB and Restart-RSQ, and establish their dynamic regrets. Based on these results, we further present a meta-algorithm that does not require any prior knowledge of the variation budget and can adaptively detect the non-stationarity on the exponential value functions. A dynamic regret lower bound is then established for non-stationary risk-sensitive RL to certify the near-optimality of the proposed algorithms. Our results also show that the risk control and the handling of the non-stationarity can be separately designed in the algorithm if the variation budget is known a prior, while the non-stationary detection mechanism in the adaptive algorithm depends on the risk parameter. This work offers the first non-asymptotic theoretical analyses for the non-stationary risk-sensitive RL in the literature.

Due to the noises in crowdsourced labels, label aggregation (LA) has emerged as a standard procedure to post-process crowdsourced labels. LA methods estimate true labels from crowdsourced labels by modeling worker qualities. Most existing LA methods are iterative in nature. They need to traverse all the crowdsourced labels multiple times in order to jointly and iteratively update true labels and worker qualities until convergence. Consequently, these methods have high space and time complexities. In this paper, we treat LA as a dynamic system and model it as a Dynamic Bayesian network. From the dynamic model we derive two light-weight algorithms, LA\textsuperscript{onepass} and LA\textsuperscript{twopass}, which can effectively and efficiently estimate worker qualities and true labels by traversing all the labels at most twice. Due to the dynamic nature, the proposed algorithms can also estimate true labels online without re-visiting historical data. We theoretically prove the convergence property of the proposed algorithms, and bound the error of estimated worker qualities. We also analyze the space and time complexities of the proposed algorithms and show that they are equivalent to those of majority voting. Experiments conducted on 20 real-world datasets demonstrate that the proposed algorithms can effectively and efficiently aggregate labels in both offline and online settings even if they traverse all the labels at most twice.

In contrast to the advances in characterizing the sample complexity for solving Markov decision processes (MDPs), the optimal statistical complexity for solving constrained MDPs (CMDPs) remains unknown. We resolve this question by providing minimax upper and lower bounds on the sample complexity for learning near-optimal policies in a discounted CMDP with access to a generative model (simulator). In particular, we design a model-based algorithm that addresses two settings: (i) relaxed feasibility, where small constraint violations are allowed, and (ii) strict feasibility, where the output policy is required to satisfy the constraint. For (i), we prove that our algorithm returns an $\epsilon$-optimal policy with probability $1 - \delta$, by making $\tilde{O}\left(\frac{S A \log(1/\delta)}{(1 - \gamma)^3 \epsilon^2}\right)$ queries to the generative model, thus matching the sample-complexity for unconstrained MDPs. For (ii), we show that the algorithm's sample complexity is upper-bounded by $\tilde{O} \left(\frac{S A \, \log(1/\delta)}{(1 - \gamma)^5 \, \epsilon^2 \zeta^2} \right)$ where $\zeta$ is the problem-dependent Slater constant that characterizes the size of the feasible region. Finally, we prove a matching lower-bound for the strict feasibility setting, thus obtaining the first near minimax optimal bounds for discounted CMDPs. Our results show that learning CMDPs is as easy as MDPs when small constraint violations are allowed, but inherently more difficult when we demand zero constraint violation.