From: Michael Orlitzky Date: Sat, 12 Nov 2016 12:39:20 +0000 (-0500) Subject: Enable the dual starting point and fix the test tolerance. X-Git-Tag: 0.1.0~31 X-Git-Url: http://gitweb.michael.orlitzky.com/?p=dunshire.git;a=commitdiff_plain;h=709cd03fff79e76f9fd78ba70711ea2694607e05 Enable the dual starting point and fix the test tolerance. We set dualstart=player2_start(), but that caused some tests to fail as unknown or optimal but not valid. So the new epsilon_scale() method is used to verify the primal/dual optimal in solution(). After that, the tests of course fail, because we're accepting much more-wrong solutions. Incorporating epsilon_scale() into the test suite fixes that. --- diff --git a/dunshire/games.py b/dunshire/games.py index ae1426a..cfb62a3 100644 --- a/dunshire/games.py +++ b/dunshire/games.py @@ -13,6 +13,7 @@ from . import options printing.options['dformat'] = options.FLOAT_FORMAT + class Solution: """ A representation of the solution of a linear game. It should contain @@ -986,6 +987,7 @@ class SymmetricLinearGame: self.A(), self.b(), primalstart=self.player1_start(), + dualstart=self.player2_start(), options=opts) except ValueError as error: if str(error) == 'math domain error': @@ -1020,6 +1022,20 @@ class SymmetricLinearGame: printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT raise GameUnsolvableException(self, soln_dict) + # For the game value, we could use any of: + # + # * p1_value + # * p2_value + # * (p1_value + p2_value)/2 + # * the game payoff + # + # We want the game value to be the payoff, however, so it + # makes the most sense to just use that, even if it means we + # can't test the fact that p1_value/p2_value are close to the + # payoff. + payoff = self.payoff(p1_optimal, p2_optimal) + soln = Solution(payoff, p1_optimal, p2_optimal) + # The "optimal" and "unknown" results, we actually treat the # same. Even if CVXOPT bails out due to numerical difficulty, # it will have some candidate points in mind. If those @@ -1030,7 +1046,8 @@ class SymmetricLinearGame: # close enough (one could be low by ABS_TOL, the other high by # it) because otherwise CVXOPT might return "unknown" and give # us two points in the cone that are nowhere near optimal. - if abs(p1_value - p2_value) > 2*options.ABS_TOL: + # + if abs(p1_value - p2_value) > self.epsilon_scale(soln)*options.ABS_TOL: printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT raise GameUnsolvableException(self, soln_dict) @@ -1040,19 +1057,7 @@ class SymmetricLinearGame: printing.options['dformat'] = options.DEBUG_FLOAT_FORMAT raise GameUnsolvableException(self, soln_dict) - # For the game value, we could use any of: - # - # * p1_value - # * p2_value - # * (p1_value + p2_value)/2 - # * the game payoff - # - # We want the game value to be the payoff, however, so it - # makes the most sense to just use that, even if it means we - # can't test the fact that p1_value/p2_value are close to the - # payoff. - payoff = self.payoff(p1_optimal, p2_optimal) - return Solution(payoff, p1_optimal, p2_optimal) + return soln def condition(self): diff --git a/test/symmetric_linear_game_test.py b/test/symmetric_linear_game_test.py index 19be8c5..067aaa1 100644 --- a/test/symmetric_linear_game_test.py +++ b/test/symmetric_linear_game_test.py @@ -137,9 +137,13 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 of the game by the same number. """ (alpha, H) = random_nn_scaling(G) - value1 = G.solution().game_value() - value2 = H.solution().game_value() - modifier = 4*max(abs(alpha), 1) + soln1 = G.solution() + soln2 = H.solution() + value1 = soln1.game_value() + value2 = soln2.game_value() + modifier1 = G.epsilon_scale(soln1) + modifier2 = H.epsilon_scale(soln2) + modifier = max(modifier1, modifier2) self.assert_within_tol(alpha*value1, value2, modifier) @@ -178,7 +182,7 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 (alpha, H) = random_translation(G) value2 = H.solution().game_value() - modifier = 4*max(abs(alpha), 1) + modifier = G.epsilon_scale(soln1) self.assert_within_tol(value1 + alpha, value2, modifier) # Make sure the same optimal pair works. @@ -221,14 +225,12 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 y_bar = soln1.player2_optimal() soln2 = H.solution() - # The modifier of 4 is because each could be off by 2*ABS_TOL, - # which is how far apart the primal/dual objectives have been - # observed being. - self.assert_within_tol(-soln1.game_value(), soln2.game_value(), 4) + mod = G.epsilon_scale(soln1) + self.assert_within_tol(-soln1.game_value(), soln2.game_value(), mod) # Make sure the switched optimal pair works. Since x_bar and # y_bar come from G, we use the same modifier. - self.assert_within_tol(soln2.game_value(), H.payoff(y_bar, x_bar), 4) + self.assert_within_tol(soln2.game_value(), H.payoff(y_bar, x_bar), mod) @@ -263,13 +265,9 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 ip1 = inner_product(y_bar, G.L()*x_bar - value*G.e1()) ip2 = inner_product(value*G.e2() - G.L().trans()*y_bar, x_bar) - # Huh.. well, y_bar and x_bar can each be epsilon away, but - # x_bar is scaled by L, so that's (norm(L) + 1), and then - # value could be off by epsilon, so that's another norm(e1) or - # norm(e2). On the other hand, this test seems to pass most of - # the time even with a modifier of one. How about.. four? - self.assert_within_tol(ip1, 0, 4) - self.assert_within_tol(ip2, 0, 4) + modifier = G.epsilon_scale(soln) + self.assert_within_tol(ip1, 0, modifier) + self.assert_within_tol(ip2, 0, modifier) def test_orthogonality_orthant(self): @@ -325,11 +323,9 @@ class SymmetricLinearGameTest(TestCase): # pylint: disable=R0904 negative_stable = all([eig < options.ABS_TOL for eig in eigs]) self.assertTrue(negative_stable) - # The dual game's value should always equal the primal's. - # The modifier of 4 is because even though the games are dual, - # CVXOPT doesn't know that, and each could be off by 2*ABS_TOL. dualsoln = G.dual().solution() - self.assert_within_tol(dualsoln.game_value(), soln.game_value(), 4) + mod = G.epsilon_scale(soln) + self.assert_within_tol(dualsoln.game_value(), soln.game_value(), mod) def test_lyapunov_orthant(self):