Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed.

The Job Shop Scheduling (JSS) problem can be viewed as an integer optimization program with linear objective function and linear, disjunctive constraints. Theconstraints(14c)enforceprecedencebetween tasks that must be scheduled in the specified order within their respective job. Themodel presented belowisusedtoconstruct solutions that are integral, and feasible tothe original problem constraints. However, the resolution frequency to solve OPFs is limited by their computational complexity. Additionally,the stochasticity introduced by renewable energy sources further increases the number of scenarios to consider. C.2 DatasetDetails Table 4 describes the power network benchmarks used, including the number of buses|N|, and transmission lines/transformers |E|.

Let w =( 1.5,0,..0) N(0,0.5) Denoting (25) utionofonwsameasthatof (26) eyobservationisthat.., Z1/2w k are Toseewhythisisthecase, wecanvectorizeeachterm: First, let' Lemma ForanyF :Rd R!R+, define problem 1,..., k, as : = su Next, let' 2021) Provingthe 31 Lf (w, b) C(w)2 n (49) tobetheleft(47)(wherethe ( (w),b)isused depends wonlythrough (w)).

Sampling is an important research problem in statistics learning with many applications such as Bayesian inference [1], multi-arm bandit optimization [2], and reinforcement learning [3].

In all cases, we show significant improvement over baselines across a varietyofMuJoCotasks.

However, numbers for BCQ and SAC are from our runs for all tasks. These plots show that, in the vast majority of environments, CDC exhibits consistently better performance across different seeds/iterations.

Despite its potential, offline RL faces twosignificant challenges that impact its performance.

If there are multiple LVs, we select the LV with the maximum probabilityp(W). It is a heuristic to improve the empirical performancesuggestedby[13]. The simulated robot pushing experiment is taken from [23]. The simulation returns the location of apushed object given the robot'slocation and the pushing duration, i.e.,x. The portfolio optimization problem is taken from [4].