Solving batches of two-player zero-sum normal-form games

nfgs.py

import numpy as np
import gurobipy
import cvxopt
from multiprocessing import Pool
from timeit import default_timer as timer

gurobipy.setParam('OutputFlag', 0)
def max_min_gurobi(game):
    model = gurobipy.Model()
    v = model.addMVar(1)
    x = model.addMVar(game.shape[0])
    model.setObjective(v.sum(), gurobipy.GRB.MAXIMIZE)
    model.addConstr(x.sum() == 1)
    model.addConstr(x >= 0)
    model.addConstrs((
        v <= game[:, i] @ x
        for i in range(game.shape[1])
    ))
    model.optimize()
    return model.objVal

cvxopt.solvers.options['glpk'] = {'msg_lev' : 'GLP_MSG_OFF'}
def max_min_cvxopt(game):
    return -cvxopt.solvers.lp(
        solver='glpk',
        c=cvxopt.matrix(-np.concatenate((np.ones(1), np.zeros(game.shape[0])))),
        G=cvxopt.matrix(np.concatenate((
            np.concatenate((
                np.eye(1)[:, :, None].repeat(game.shape[1], 2),
                -game[None],
            ), 1).swapaxes(1, 2).reshape(game.shape[1], 1 + game.shape[0]),
            -np.eye(1 + game.shape[0])[1:]
        ), 0)),
        h=cvxopt.matrix(np.zeros(game.shape[1] + game.shape[0])),
        A=cvxopt.matrix(np.concatenate((np.zeros(1), np.ones(game.shape[0])))[None]),
        b=cvxopt.matrix(np.ones(1))
    )['primal objective']

pool = Pool()
def max_min(game_batch, method):
    return np.array(pool.map(method, game_batch))

rng = np.random.default_rng()
while True:
    game_batch = rng.uniform(size=(20, 30, 40))
    start = timer()
    v_gurobi = max_min(game_batch, max_min_gurobi)
    t_gurobi = timer() - start
    start = timer()
    v_cvxopt = max_min(game_batch, max_min_cvxopt)
    t_cvxopt = timer() - start
    assert np.allclose(v_gurobi, v_cvxopt)
    print('gurobi {}\ncvxopt {}\n'.format(t_gurobi, t_cvxopt))