The evolution and growing automation of collaborative robots introduce more complexity and unpredictability to systems, highlighting the crucial need for robot's adaptability and flexibility to address the increasing complexities of their environment. In typical industrial production scenarios, robots are often required to be re-programmed when facing a more demanding task or even a few changes in workspace conditions. To increase productivity, efficiency and reduce human effort in the design process, this paper explores the potential of using digital twin combined with Reinforcement Learning (RL) to enable robots to generate self-improving collision-free trajectories in real time. The digital twin, acting as a virtual counterpart of the physical system, serves as a 'forward run' for monitoring, controlling, and optimizing the physical system in a safe and cost-effective manner. The physical system sends data to synchronize the digital system through the video feeds from cameras, which allows the virtual robot to update its observation and policy based on real scenarios. The bidirectional communication between digital and physical systems provides a promising platform for hardware-in-the-loop RL training through trial and error until the robot successfully adapts to its new environment. The proposed online training framework is demonstrated on the Unfactory Xarm5 collaborative robot, where the robot end-effector aims to reach the target position while avoiding obstacles. The experiment suggest that proposed framework is capable of performing policy online training, and that there remains significant room for improvement.

We propose an online prediction version of submodular set cover with connections to ranking and repeated active learning. In each round, the learning algorithm chooses a sequence of items. The algorithm then receives a monotone submodular function and suffers loss equal to the cover time of the function: the number of items needed, when items are selected in order of the chosen sequence, to achieve a coverage constraint. We develop an online learning algorithm whose loss converges to approximately that of the best sequence in hindsight. Our proposed algorithm is readily extended to a setting where multiple functions are revealed at each round and to bandit and contextual bandit settings.

Learning theory has largely focused on two main learning scenarios: the classical statistical setting where instances are drawn i.i.d.

Most methods for decision-theoretic online learning are based on the Hedge algorithm, which takes a parameter called the learning rate. In most previous analyses the learning rate was carefully tuned to obtain optimal worst-case performance, leading to suboptimal performance on easy instances, for example when there exists an action that is significantly better than all others. We propose a new way of setting the learning rate, which adapts to the difficulty of the learning problem: in the worst case our procedure still guarantees optimal performance, but on easy instances it achieves much smaller regret. In particular, our adaptive method achieves constant regret in a probabilistic setting, when there exists an action that on average obtains strictly smaller loss than all other actions. We also provide a simulation study comparing our approach to existing methods.

Most online algorithms used in machine learning today are based on variants of mirror descent or follow-the-leader. In this paper, we present an online algorithm based on a completely different approach, which combines "random playout" and randomized rounding of loss subgradients. As an application of our approach, we provide the first computationally efficient online algorithm for collaborative filtering with trace-norm constrained matrices. As a second application, we solve an open question linking batch learning and transductive online learning.

This paper provides the first --to the best of our knowledge-- analysis of online learning algorithms for multiclass problems when the confusion matrix is taken as a performance measure. The work builds upon recent and elegant results on noncommutative concentration inequalities, i.e. concentration inequalities that apply to matrices, and, more precisely, to matrix martingales. We do establish generalization bounds for online learning algorithms and show how the theoretical study motivates the proposition of a new confusion-friendly learning procedure. This learning algorithm, called COPA (for COnfusion Passive-Aggressive) is a passive-aggressive learning algorithm; it is shown that the update equations for COPA can be computed analytically and, henceforth, there is no need to recourse to any optimization package to implement it.

We consider a popular problem in finance, option pricing, through the lens of an online learning game between Nature and an Investor. In the Black-Scholes option pricing model from 1973, the Investor can continuously hedge the risk of an option by trading the underlying asset, assuming that the asset's price fluctuates according to Geometric Brownian Motion (GBM). We consider a worst-case model, in which Nature chooses a sequence of price fluctuations under a cumulative quadratic volatility constraint, and the Investor can make a sequence of hedging decisions. Our main result is to show that the value of our proposed game, which is the "regret" of hedging strategy, converges to the Black-Scholes option price. We use significantly weaker assumptions than previous work--for instance, we allow large jumps in the asset price--and show that the Black-Scholes hedging strategy is near-optimal for the Investor even in this non-stochastic framework.

We provide several applications of Optimistic Mirror Descent, an online learning algorithm based on the idea of predictable sequences. First, we recover the Mirror Prox algorithm for offline optimization, prove an extension to Hölder-smooth functions, and apply the results to saddle-point type problems. Next, we prove that a version of Optimistic Mirror Descent (which has a close relation to the Exponential Weights algorithm) can be used by two strongly-uncoupled players in a finite zero-sum matrix game to converge to the minimax equilibrium at the rate of O((log T) T).

We give differentially private algorithms for a large class of online learning algorithms, in both the full information and bandit settings. Our algorithms aim to minimize a convex loss function which is a sum of smaller convex loss terms, one for each data point. To design our algorithms, we modify the popular mirror descent approach, or rather a variant called follow the approximate leader. The technique leads to the first nonprivate algorithms for private online learning in the bandit setting. In the full information setting, our algorithms improve over the regret bounds of previous work (due to Dwork, Naor, Pitassi and Rothblum (2010) and Jain, Kothari and Thakurta (2012)). In many cases, our algorithms (in both settings) match the dependence on the input length, T, of the optimal nonprivate regret bounds up to logarithmic factors in T. Our algorithms require logarithmic space and update time.

We study the power of different types of adaptive (nonoblivious) adversaries in the setting of prediction with expert advice, under both full-information and bandit feedback. We measure the player's performance using a new notion of regret, also known as policy regret, which better captures the adversary's adaptiveness to the player's behavior. In a setting where losses are allowed to drift, we characterize --in a nearly complete manner-- the power of adaptive adversaries with bounded memories and switching costs.