  This paper develops a machine learning-driven portfolio optimization
framework for virtual bidding in electricity markets considering both risk
constraint and price sensitivity. The algorithmic trading strategy is developed
from the perspective of a proprietary trading firm to maximize profit. A
recurrent neural network-based Locational Marginal Price (LMP) spread forecast
model is developed by leveraging the inter-hour dependencies of the market
clearing algorithm. The LMP spread sensitivity with respect to net virtual bids
is modeled as a monotonic function with the proposed constrained gradient
boosting tree. We leverage the proposed algorithmic virtual bid trading
strategy to evaluate both the profitability of the virtual bid portfolio and
the efficiency of U.S. wholesale electricity markets. The comprehensive
empirical analysis on PJM, ISO-NE, and CAISO indicates that the proposed
virtual bid portfolio optimization strategy considering the price sensitivity
explicitly outperforms the one that neglects the price sensitivity. The Sharpe
ratio of virtual bid portfolios for all three electricity markets are much
higher than that of the S&P 500 index. It was also shown that the efficiency of
CAISO's two-settlement system is lower than that of PJM and ISO-NE.
