This research is motivated by virtual tolling agreements, financial derivatives products in the energy market. The product involves nominating the operational regimes to the asset owner by the contract holder. By introducing a family of martingale penalties, we develop a duality theory for finite-horizon optimal multiple switching with discrete intervention dates on a general filtration, allowing continuous-time observations between decision dates. The minimal penalty is characterized by the Doob martingales of the continuation values, which yields a fully computable genuine upper bound. In the Brownian Markovian setting, the martingale integrand yields hedge sensitivities and admits a natural delta-hedging interpretation. We then extend DeepMartingale from optimal stopping to optimal switching and establish convergence under both the upper-bound loss and an $L^2$-surrogate loss. We also provide an expressivity analysis. Hence, at the level of approximation expressivity, the dual solver avoids the curse of dimensionality under the stated structural assumptions. For numerical validation, we additionally implement an auxiliary policy-based approach to produce feasible lower bounds and empirical upper--lower gaps. Numerical experiments on Brownian models and a Brownian--Poisson extension illustrate small upper--lower gaps, favorable high-dimensional performance, and the hedging information produced by the learned dual martingales.