Rewards are a critical aspect of formulating Reinforcement Learning (RL) problems; often, one may be interested in testing multiple reward functions, or the problem may naturally involve multiple rewards. In this study, we investigate the _Multi-Reward Best Policy Identification_ (MR-BPI) problem, where the goal is to determine the best policy for all rewards in a given set $\mathcal{R}$ with minimal sample complexity and a prescribed confidence level. We derive a fundamental instance-specific lower bound on the sample complexity required by any Probably Correct (PC) algorithm in this setting. This bound guides the design of an optimal exploration policy attaining minimal sample complexity. However, this lower bound involves solving a hard non-convex optimization problem. We address this challenge by devising a convex approximation, enabling the design of sample-efficient algorithms. We propose MR-NaS, a PC algorithm with competitive performance on hard-exploration tabular environments. Extending this approach to Deep RL (DRL), we also introduce DBMR-BPI, an efficient algorithm for model-free exploration in multi-reward settings.

Controlling antenna tilts in cellular networks is critical to achieve a good trade-off between network coverage and capacity. We devise algorithms learning optimal tilt control policies from existing data (passive learning setting) or from data actively generated by the algorithms (active learning setting). We formalize the design of such algorithms as a Best Policy Identification problem in Contextual Linear Bandits (CLB). In CLB, an action represents an antenna tilt update; the context captures current network conditions; the reward corresponds to an improvement of performance, mixing coverage and capacity. The objective is to identify an approximately optimal policy (a function mapping the context to an action with maximal reward). For both active and passive learning, we derive information-theoretical lower bounds on the number of samples required by any algorithm returning an approximately optimal policy with a given level of certainty, and devise algorithms achieving these fundamental limits. We apply our algorithms to the Remote Electrical Tilt optimization problem in cellular networks, and show that they can produce optimal tilt update policy using much fewer data samples than naive or existing rule-based learning algorithms. This paper is an extension of work presented at IEEE International Conference on Computer Communications (INFOCOM) 2022 (Vannella et al. 2022).

We investigate the problem of best arm identification in Multi-Agent Multi-Armed Bandits (MAMABs) where the rewards are defined through a factor graph. The objective is to find an optimal global action with a prescribed level of confidence and minimal sample complexity. We derive a tight instance-specific lower bound of the sample complexity and characterize the corresponding optimal sampling strategy. Unfortunately, this bound is obtained by solving a combinatorial optimization problem with a number of variables and constraints exponentially growing with the number of agents. We leverage Mean Field (MF) techniques to obtain, in a computationally efficient manner, an approximation of the lower bound. The approximation scales at most as $\rho K^d$ (where $\rho$, $K$, and $d$ denote the number of factors in the graph, the number of possible actions per agent, and the maximal degree of the factor graph). We devise MF-TaS (Mean-Field-Track-and-Stop), an algorithm whose sample complexity provably matches our approximated lower bound. We illustrate the performance of MF-TaS numerically using both synthetic and real-world experiments (e.g., to solve the antenna tilt optimization problem in radio communication networks).

We study the problem of regret minimization in Multi-Agent Multi-Armed Bandits (MAMABs) where the rewards are defined through a factor graph. We derive an instance-specific regret lower bound and characterize the minimal expected number of times each global action should be explored. Unfortunately, this bound and the corresponding optimal exploration process are obtained by solving a combinatorial optimization problem with a set of variables and constraints exponentially growing with the number of agents. We approximate the regret lower bound problem via Mean Field techniques to reduce the number of variables and constraints. By tuning the latter, we explore the trade-off between achievable regret and complexity. We devise Efficient Sampling for MAMAB (ESM), an algorithm whose regret asymptotically matches the corresponding approximated lower bound. We assess the regret and computational complexity of ESM numerically, using both synthetic and real-world experiments in radio communications networks.

Controlling antenna tilts in cellular networks is imperative to reach an efficient trade-off between network coverage and capacity. In this paper, we devise algorithms learning optimal tilt control policies from existing data (in the so-called passive learning setting) or from data actively generated by the algorithms (the active learning setting). We formalize the design of such algorithms as a Best Policy Identification (BPI) problem in Contextual Linear Multi-Arm Bandits (CL-MAB). An arm represents an antenna tilt update; the context captures current network conditions; the reward corresponds to an improvement of performance, mixing coverage and capacity; and the objective is to identify, with a given level of confidence, an approximately optimal policy (a function mapping the context to an arm with maximal reward). For CL-MAB in both active and passive learning settings, we derive information-theoretical lower bounds on the number of samples required by any algorithm returning an approximately optimal policy with a given level of certainty, and devise algorithms achieving these fundamental limits. We apply our algorithms to the Remote Electrical Tilt (RET) optimization problem in cellular networks, and show that they can produce optimal tilt update policy using much fewer data samples than naive or existing rule-based learning algorithms.

Safe interaction with the environment is one of the most challenging aspects of Reinforcement Learning (RL) when applied to real-world problems. This is particularly important when unsafe actions have a high or irreversible negative impact on the environment. In the context of network management operations, Remote Electrical Tilt (RET) optimisation is a safety-critical application in which exploratory modifications of antenna tilt angles of base stations can cause significant performance degradation in the network. In this paper, we propose a modular Safe Reinforcement Learning (SRL) architecture which is then used to address the RET optimisation in cellular networks. In this approach, a safety shield continuously benchmarks the performance of RL agents against safe baselines, and determines safe antenna tilt updates to be performed on the network. Our results demonstrate improved performance of the SRL agent over the baseline while ensuring the safety of the performed actions.

Remote Electrical Tilt (RET) optimization is an efficient method for adjusting the vertical tilt angle of Base Stations (BSs) antennas in order to optimize Key Performance Indicators (KPIs) of the network. Reinforcement Learning (RL) provides a powerful framework for RET optimization because of its self-learning capabilities and adaptivity to environmental changes. However, an RL agent may execute unsafe actions during the course of its interaction, i.e., actions resulting in undesired network performance degradation. Since the reliability of services is critical for Mobile Network Operators (MNOs), the prospect of performance degradation has prohibited the real-world deployment of RL methods for RET optimization. In this work, we model the RET optimization problem in the Safe Reinforcement Learning (SRL) framework with the goal of learning a tilt control strategy providing performance improvement guarantees with respect to a safe baseline. We leverage a recent SRL method, namely Safe Policy Improvement through Baseline Bootstrapping (SPIBB), to learn an improved policy from an offline dataset of interactions collected by the safe baseline. Our experiments show that the proposed approach is able to learn a safe and improved tilt update policy, providing a higher degree of reliability and potential for real-world network deployment.

We address the problem of Remote Electrical Tilt (RET) optimization using off-policy Contextual Multi-Armed-Bandit (CMAB) techniques. The goal in RET optimization is to control the orientation of the vertical tilt angle of the antenna to optimize Key Performance Indicators (KPIs) representing the Quality of Service (QoS) perceived by the users in cellular networks. Learning an improved tilt update policy is hard. On the one hand, coming up with a new policy in an online manner in a real network requires exploring tilt updates that have never been used before, and is operationally too risky. On the other hand, devising this policy via simulations suffers from the simulation-to-reality gap. In this paper, we circumvent these issues by learning an improved policy in an offline manner using existing data collected on real networks. We formulate the problem of devising such a policy using the off-policy CMAB framework. We propose CMAB learning algorithms to extract optimal tilt update policies from the data. We train and evaluate these policies on real-world 4G Long Term Evolution (LTE) cellular network data. Our policies show consistent improvements over the rule-based logging policy used to collect the data.