This article introduces the concepts around Online Bandit Linear Optimization and explores an efficient setup called SCRiBLe (Self-Concordant Regularization in Bandit Learning) created by Abernethy et. al.\cite{abernethy}. The SCRiBLe setup and algorithm yield a $O(\sqrt{T})$ regret bound and polynomial run time complexity bound on the dimension of the input space. In this article we build up to the bandit linear optimization case and study SCRiBLe.

In the context of machine learning, disparate impact refers to a form of systematic discrimination whereby the output distribution of a model depends on the value of a sensitive attribute (e.g., race or gender). In this paper, we propose an information-theoretic framework to analyze the disparate impact of a binary classification model. We view the model as a fixed channel, and quantify disparate impact as the divergence in output distributions over two groups. Our aim is to find a correction function that can perturb the input distributions of each group to align their output distributions. We present an optimization problem that can be solved to obtain a correction function that will make the output distributions statistically indistinguishable. We derive closed-form expressions to efficiently compute the correction function, and demonstrate the benefits of our framework on a recidivism prediction problem based on the ProPublica COMPAS dataset.

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.

We propose an algorithm for constructing efficient patrolling strategies in the Internet environment, where the protected targets are nodes connected to the network and the patrollers are software agents capable of detecting/preventing undesirable activities on the nodes. The algorithm is based on a novel compositional principle designed for a special class of strategies, and it can quickly construct (sub)optimal solutions even if the number of targets reaches hundreds of millions.

Using AI approaches to automatically design mechanisms has been a central research mission at the interface of AI and economics [Conitzer and Sandholm, 2002]. Previous approaches that a empt to design revenue optimal auctions for the multi-dimensional settings fall short in at least one of the three aspects: 1) representation --- search in a space that probably does not even contain the optimal mechanism; 2) exactness --- finding a mechanism that is either not truthful or far from optimal; 3) domain dependence --- need a different design for different environment settings. To resolve the three difficulties, in this paper, we put forward a uni ed neural network based framework that automatically learns to design revenue optimal mechanisms. Our framework consists of a mechanism network that takes an input distribution for training and outputs a mechanism, as well as a buyer network that takes a mechanism as input and output an action. Such a separation in design mitigates the difficulty to impose incentive compatibility constraints on the mechanism, by making it a rational choice of the buyer. As a result, our framework easily overcomes the previously mentioned difficulty in incorporating IC constraints and always returns exactly incentive compatible mechanisms. We then applied our framework to a number of multi-item revenue optimal design settings, for a few of which the theoretically optimal mechanisms are unknown. We then go on to theoretically prove that the mechanisms found by our framework are indeed optimal.

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the discrete view has its intrinsic limitations: there is no characterization of the optimization path and the proof techniques are induction-based and thus usually complicated. Inspired by the recent successful adoptions of stochastic differential equations (SDE) to the theoretical analysis of SGD, in this paper, we study the continuous approximation of ASGD by using stochastic differential delay equations (SDDE). We introduce the approximation method and study the approximation error. Then we conduct theoretical analysis on the convergence rates of ASGD algorithm based on the continuous approximation. There are two methods: moment estimation and energy function minimization can be used to analyze the convergence rates. Moment estimation depends on the specific form of the loss function, while energy function minimization only leverages the convex property of the loss function, and does not depend on its specific form. In addition to the convergence analysis, the continuous view also helps us derive better convergence rates. All of this clearly shows the advantage of taking the continuous view in gradient descent algorithms.

In my previous article, I described why we need to get incentives right when we build tokenized ecosystems. Here, I ask: how do we design incentives for these tokenized ecosystems? And actually since incentives are the heart of tokenized ecosystems, it's really: how do we design tokenized ecosystems? And, how do we analyze and verify them? This article is a first stake in the ground towards a practice of token engineering: the theory, practice and tools to analyze, design, and verify tokenized ecosystems. The first section of this article relates token designs to other fields and explains why "engineering". This section relates token design to other fields. How did the bridge collapse? The designers did anticipate for wind, after all. However, they failed to anticipate that the particular wind patterns would set up resonance with the bridge itself.

In many practical uses of reinforcement learning (RL) the set of actions available at a given state is a random variable, with realizations governed by an exogenous stochastic process. Somewhat surprisingly, the foundations for such sequential decision processes have been unaddressed. In this work, we formalize and investigate MDPs with stochastic action sets (SAS-MDPs) to provide these foundations. We show that optimal policies and value functions in this model have a structure that admits a compact representation. From an RL perspective, we show that Q-learning with sampled action sets is sound. In model-based settings, we consider two important special cases: when individual actions are available with independent probabilities; and a sampling-based model for unknown distributions. We develop poly-time value and policy iteration methods for both cases; and in the first, we offer a poly-time linear programming solution.

This paper presents a method for identifying mechanical parameters of robots or objects, such as their mass and friction coefficients. Key features are the use of off-the-shelf physics engines and the adaptation of a Bayesian optimization technique towards minimizing the number of real-world experiments needed for model-based reinforcement learning. The proposed framework reproduces in a physics engine experiments performed on a real robot and optimizes the model's mechanical parameters so as to match real-world trajectories. The optimized model is then used for learning a policy in simulation, before real-world deployment. It is well understood, however, that it is hard to exactly reproduce real trajectories in simulation. Moreover, a near-optimal policy can be frequently found with an imperfect model. Therefore, this work proposes a strategy for identifying a model that is just good enough to approximate the value of a locally optimal policy with a certain confidence, instead of wasting effort on identifying the most accurate model. Evaluations, performed both in simulation and on a real robotic manipulation task, indicate that the proposed strategy results in an overall time-efficient, integrated model identification and learning solution, which significantly improves the data-efficiency of existing policy search algorithms.

Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision making under uncertainty. The classical approaches for solving MDPs are well known and have been widely studied, some of which rely on approximation techniques to solve MDPs with large state space and/or action space. However, most of these classical solution approaches and their approximation techniques still take much computation time to converge and usually must be re-computed if the reward function is changed. This paper introduces a novel alternative approach for exactly and efficiently solving deterministic, continuous MDPs with sparse reward sources. When the environment is such that the "distance" between states can be determined in constant time, e.g. grid world, our algorithm offers $O( |R|^2 \times |A|^2 \times |S|)$, where $|R|$ is the number of reward sources, $|A|$ is the number of actions, and $|S|$ is the number of states. Memory complexity for the algorithm is $O( |S| + |R| \times |A|)$. This new approach opens new avenues for boosting computational performance for certain classes of MDPs and is of tremendous value for MDP applications such as robotics and unmanned systems. This paper describes the algorithm and presents numerical experiment results to demonstrate its powerful computational performance. We also provide rigorous mathematical description of the approach.