Robust approachability and regret minimization in games with partial monitoring

Approachability has become a standard tool in analyzing earning algorithms in the adversarial online learning setup. We develop a variant of approachability for games where there is ambiguity in the obtained reward that belongs to a set, rather than being a single vector. Using this variant we tackle the problem of approachability in games with partial monitoring and develop simple and efficient algorithms (i.e., with constant per-step complexity) for this setup. We finally consider external regret and internal regret in repeated games with partial monitoring and derive regret-minimizing strategies based on approachability theory

Adaptive Power Allocation and Control in Time-Varying Multi-Carrier MIMO Networks

In this paper, we examine the fundamental trade-off between radiated power and achieved throughput in wireless multi-carrier, multiple-input and multiple-output (MIMO) systems that vary with time in an unpredictable fashion (e.g. due to changes in the wireless medium or the users' QoS requirements). Contrary to the static/stationary channel regime, there is no optimal power allocation profile to target (either static or in the mean), so the system's users must adapt to changes in the environment "on the fly", without being able to predict the system's evolution ahead of time. In this dynamic context, we formulate the users' power/throughput trade-off as an online optimization problem and we provide a matrix exponential learning algorithm that leads to no regret - i.e. the proposed transmit policy is asymptotically optimal in hindsight, irrespective of how the system evolves over time. Furthermore, we also examine the robustness of the proposed algorithm under imperfect channel state information (CSI) and we show that it retains its regret minimization properties under very mild conditions on the measurement noise statistics. As a result, users are able to track the evolution of their individually optimum transmit profiles remarkably well, even under rapidly changing network conditions and high uncertainty. Our theoretical analysis is validated by extensive numerical simulations corresponding to a realistic network deployment and providing further insights in the practical implementation aspects of the proposed algorithm.Comment: 25 pages, 4 figure

Distributed stochastic optimization via matrix exponential learning

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.Comment: 31 pages, 3 figure

A Competition-based Pricing Strategy in Cloud Markets using Regret Minimization Techniques

Cloud computing as a fairly new commercial paradigm, widely investigated by different researchers, already has a great range of challenges. Pricing is a major problem in Cloud computing marketplace; as providers are competing to attract more customers without knowing the pricing policies of each other. To overcome this lack of knowledge, we model their competition by an incomplete-information game. Considering the issue, this work proposes a pricing policy related to the regret minimization algorithm and applies it to the considered incomplete-information game. Based on the competition based marketplace of the Cloud, providers update the distribution of their strategies using the experienced regret. The idea of iteratively applying the algorithm for updating probabilities of strategies causes the regret get minimized faster. The experimental results show much more increase in profits of the providers in comparison with other pricing policies. Besides, the efficiency of a variety of regret minimization techniques in a simulated marketplace of Cloud are discussed which have not been observed in the studied literature. Moreover, return on investment of providers in considered organizations is studied and promising results appeared

A Game of Competition for Risk

In this study, we present models where participants strategically select their risk levels and earn corresponding rewards, mirroring real-world competition across various sectors. Our analysis starts with a normal form game involving two players in a continuous action space, confirming the existence and uniqueness of a Nash equilibrium and providing an analytical solution. We then extend this analysis to multi-player scenarios, introducing a new numerical algorithm for its calculation. A key novelty of our work lies in using regret minimization algorithms to solve continuous games through discretization. This groundbreaking approach enables us to incorporate additional real-world factors like market frictions and risk correlations among firms. We also experimentally validate that the Nash equilibrium in our model also serves as a correlated equilibrium. Our findings illuminate how market frictions and risk correlations affect strategic risk-taking. We also explore how policy measures can impact risk-taking and its associated rewards, with our model providing broader applicability than the Diamond-Dybvig framework. We make our methodology and open-source code available at https://github.com/louisabraham/cfrgame Finally, we contribute methodologically by advocating the use of algorithms in economics, shifting focus from finite games to games with continuous action sets. Our study provides a solid framework for analyzing strategic interactions in continuous action games, emphasizing the importance of market frictions, risk correlations, and policy measures in strategic risk-taking dynamics