An Online Approach to D2D Trajectory Utility Maximization Problem

Abstract

This paper considers the problem of designing the user trajectory in a device-to-device communications setting. We consider a pair of pedestrians connected through a D2D link. The pedestrians seek to reach their respective destinations, while using the D2D link for data exchange applications such as file transfer, video calling, and online gaming. In order to enable better D2D connectivity, the pedestrians are willing to deviate from their respective shortest paths, at the cost of reaching their destinations slightly late. A generic trajectory optimization problem is formulated and solved for the case when full information about the problem in known in advance.Motivated by the D2D user's need to keep their destinations private, we also formulate a regularized variant of the problem that can be used to develop a fully online algorithm. The proposed online algorithm is quite efficient, and is shown to achieve a sublinear offline regret while satisfying the required mobility constraints exactly. The theoretical results are backed by detailed numerical tests that establish the efficacy of the proposed algorithms under various settings.

Online Trajectory Optimization Using Inexact Gradient Feedback for Time-Varying Environments

“…Subsequently, the online formalism is used to develop the proposed algorithm and establish that it achieves sublinear regret. The algorithm and formulation in this section build upon the trajectory design problem considered by [18] in the context of communication networks. The analysis here considers a more general class of time-varying constraints and is therefore applicable to a wider variety of trajectory planning problems.…”

“…Proof sketch: The proof of Theorem 1 follows along the lines of that in [18] but includes modifications required to handle the generic time-varying convex constraint function g t and the noisy gradient feedback. It is remarked that the modification from [18] is not trivial and changes the proof as well as the final result considerably.…”

“…Contributions: The main contributions of this work include (a) development and analysis of the generic time-varying utility-optimal trajectory design problem; (b) performance analysis of the proposed IOGA algorithm for the case of timevarying objective and constraint functions, yielding a sublinear regret; (c) formulation and detailed study of the online trajectory design problem for a watercraft operating under strong ocean currents; (d) solving D2D trajectory planning problem using IOGA, by considering the uncertainty in user's positional estimates. This problem is inspired from [18], where the D2D trajectory optimization problem is formulated for the first time and solved using online gradient descent (OGD) under noiseless feedback ignoring real world uncertainties. The problem formulation in this work is different from [18] and is considered within a more general context where more realistic time-varying constraints are now included.…”

“…This problem is inspired from [18], where the D2D trajectory optimization problem is formulated for the first time and solved using online gradient descent (OGD) under noiseless feedback ignoring real world uncertainties. The problem formulation in this work is different from [18] and is considered within a more general context where more realistic time-varying constraints are now included. In addition, we propose to solve the problem in an online fashion under noisy gradient feedback and refer to it as IOGA.…”

“…Additionally, we derive lower bound to the offline dynamic regret that helps in deciding the optimality of any online policy. Next, the IOGA parameters are designed for the more sophisticated energy-efficient trajectory design problem not considered in [18]. The performance of the proposed algorithm is tested on real-world ocean current data and is shown to be significantly better than the state-of-the-art algorithms.…”