We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $\Omega(\sqrt{T})$ for any strategy, we conclude that DPDS is order optimal up to a $\sqrt{\log{T}}$ term. We evaluate the performance of DPDS empirically in the context of virtual trading in wholesale electricity markets by using historical data from the New York market. Empirical results show that DPDS consistently outperforms benchmark heuristic methods that are derived from machine learning and online learning approaches.

Automatic bidding has become one of the main options for advertisers to buy advertisement opportunities in the online advertising market [Dolan, 2020].

Automatic bidding has become one of the main options for advertisers to buy advertisement opportunities in the online advertising market [Dolan, 2020].

This paper studies the online learning (stochastic and full-information) problem of bidding in multi commodity first price auctions. The paper introduces a polynomial time algorithm that achieves a regret of \sqrt{T log(T)} that has a near optimal dependence on T. The main challenge that the paper has to deal with is to find a computationally efficient algorithm for computing the best biding strategy given a known distribution.The authors first demonstrate that natural approaches for solving this problem exactly are not computationally efficient (this is not a formal np-hardness proof). Then, they provide a FPTAS for solving the problem using dynamic programming. Once they have a FPTAS for the offline problem, their results hold for the stochastic online setting using existing reductions. I haven't carefully looked in to the details of their analysis of the dynamic programming, but I think the effectiveness of it here is interesting and surprising -- specially given that the variation of this problem for the second price auctions is hard to approximate.

Finding optimal bidding strategies for generation units in electricity markets would result in higher profit. However, it is a challenging problem due to the system uncertainty which is due to the unknown other generation units' strategies. Distributed optimization, where each entity or agent decides on its bid individually, has become state of the art. However, it cannot overcome the challenges of system uncertainties. Deep reinforcement learning is a promising approach to learn the optimal strategy in uncertain environments. Nevertheless, it is not able to integrate the information on the spatial system topology in the learning process. This paper proposes a distributed learning algorithm based on deep reinforcement learning (DRL) combined with a graph convolutional neural network (GCN). In fact, the proposed framework helps the agents to update their decisions by getting feedback from the environment so that it can overcome the challenges of the uncertainties. In this proposed algorithm, the state and connection between nodes are the inputs of the GCN, which can make agents aware of the structure of the system. This information on the system topology helps the agents to improve their bidding strategies and increase the profit. We evaluate the proposed algorithm on the IEEE 30-bus system under different scenarios. Also, to investigate the generalization ability of the proposed approach, we test the trained model on IEEE 39-bus system. The results show that the proposed algorithm has more generalization abilities compare to the DRL and can result in higher profit when changing the topology of the system.

In real time electricity markets, the objective of generation companies while bidding is to maximize their profit. The strategies for learning optimal bidding have been formulated through game theoretical approaches and stochastic optimization problems. Similar studies in reactive power markets have not been reported so far because the network voltage operating conditions have an increased impact on reactive power markets than on active power markets. Contrary to active power markets, the bids of rivals are not directly related to fuel costs in reactive power markets. Hence, the assumption of a suitable probability distribution function is unrealistic, making the strategies adopted in active power markets unsuitable for learning optimal bids in reactive power market mechanisms. Therefore, a bidding strategy is to be learnt from market observations and experience in imperfect oligopolistic competition-based markets. In this paper, a pioneer work on learning optimal bidding strategies from observation and experience in a three-stage reactive power market is reported.

We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding strategy, we propose a polynomial-time algorithm, inspired by the dynamic programming approach to the knapsack problem. The proposed algorithm, referred to as dynamic programming on discrete set (DPDS), achieves a regret order of $O(\sqrt{T\log{T}})$. By showing that the regret is lower bounded by $\Omega(\sqrt{T})$ for any strategy, we conclude that DPDS is order optimal up to a $\sqrt{\log{T}}$ term.