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HeuristicLab.Problems.DataAnalysis.Regression.Symbolic.Extensions

Timestamp:

08/13/19 19:02:57 (5 years ago)

Author:

gkronber

Message:

#2994: use new code for NLOpt in the NLOpt evaluator

File:

: 1 edited

branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Regression.Symbolic.Extensions/NLOptEvaluator.cs (modified) (2 diffs)

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branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Regression.Symbolic.Extensions/NLOptEvaluator.cs

-                      r17196
+                      r17215
+    }
-    // for data exchange to/from optimizer in native code
-    [StructLayout(LayoutKind.Sequential)]
-    private struct ConstraintData {
-      public ISymbolicExpressionTree Tree;
-      public ISymbolicExpressionTreeNode[] ParameterNodes;
+    }
     public static double OptimizeConstants(ISymbolicDataAnalysisExpressionTreeInterpreter interpreter,
 …
       if (!applyLinearScaling) throw new NotSupportedException("application without linear scaling is not supported");
+      // we always update constants, so we don't need to calculate initial quality
+      // double originalQuality = SymbolicRegressionSingleObjectiveMeanSquaredErrorEvaluator.Calculate(interpreter, tree, lowerEstimationLimit, upperEstimationLimit, problemData, rows, applyLinearScaling: false);
+      if (counter == null) counter = new EvaluationsCounter();
+      var rowEvaluationsCounter = new EvaluationsCounter();
+      var intervalConstraints = problemData.IntervalConstraints;
+      var dataIntervals = problemData.VariableRanges.GetIntervals();
+      var trainingRows = problemData.TrainingIndices.ToArray();
+      // buffers
+      var target = problemData.TargetVariableTrainingValues.ToArray();
+      var targetStDev = target.StandardDeviationPop();
+      var targetVariance = targetStDev * targetStDev;
+      var targetMean = target.Average();
+      var pred = interpreter.GetSymbolicExpressionTreeValues(tree, problemData.Dataset, trainingRows).ToArray();
+      if (pred.Any(pi => double.IsInfinity(pi) || double.IsNaN(pi))) return targetVariance;
+      #region linear scaling
+      var predStDev = pred.StandardDeviationPop();
+      if (predStDev == 0) return targetVariance; // constant expression
+      var predMean = pred.Average();
+      var scalingFactor = targetStDev / predStDev;
+      var offset = targetMean - predMean * scalingFactor;
+      ISymbolicExpressionTree scaledTree = null;
+      if (applyLinearScaling) scaledTree = CopyAndScaleTree(tree, scalingFactor, offset);
+      #endregion
+      // convert constants to variables named theta...
+      var treeForDerivation = ReplaceConstWithVar(scaledTree, out List<string> thetaNames, out List<double> thetaValues); // copies the tree
+      // create trees for relevant derivatives
+      Dictionary<string, ISymbolicExpressionTree> derivatives = new Dictionary<string, ISymbolicExpressionTree>();
+      var allThetaNodes = thetaNames.Select(_ => new List<ConstantTreeNode>()).ToArray();
+      var constraintTrees = new List<ISymbolicExpressionTree>();
+      foreach (var constraint in intervalConstraints.Constraints) {
+        if (constraint.IsDerivation) {
+          if (!problemData.AllowedInputVariables.Contains(constraint.Variable))
+            throw new ArgumentException($"Invalid constraint: the variable {constraint.Variable} does not exist in the dataset.");
+          var df = DerivativeCalculator.Derive(treeForDerivation, constraint.Variable);
+          // alglib requires constraint expressions of the form c(x) <= 0
+          // -> we make two expressions, one for the lower bound and one for the upper bound
+          if (constraint.Interval.UpperBound < double.PositiveInfinity) {
+            var df_smaller_upper = Subtract((ISymbolicExpressionTree)df.Clone(), CreateConstant(constraint.Interval.UpperBound));
+            // convert variables named theta back to constants
+            var df_prepared = ReplaceVarWithConst(df_smaller_upper, thetaNames, thetaValues, allThetaNodes);
+            constraintTrees.Add(df_prepared);
+          }
+          if (constraint.Interval.LowerBound > double.NegativeInfinity) {
+            var df_larger_lower = Subtract(CreateConstant(constraint.Interval.LowerBound), (ISymbolicExpressionTree)df.Clone());
+            // convert variables named theta back to constants
+            var df_prepared = ReplaceVarWithConst(df_larger_lower, thetaNames, thetaValues, allThetaNodes);
+            constraintTrees.Add(df_prepared);
+          }
+        } else {
+          if (constraint.Interval.UpperBound < double.PositiveInfinity) {
+            var f_smaller_upper = Subtract((ISymbolicExpressionTree)treeForDerivation.Clone(), CreateConstant(constraint.Interval.UpperBound));
+            // convert variables named theta back to constants
+            var df_prepared = ReplaceVarWithConst(f_smaller_upper, thetaNames, thetaValues, allThetaNodes);
+            constraintTrees.Add(df_prepared);
+          }
+          if (constraint.Interval.LowerBound > double.NegativeInfinity) {
+            var f_larger_lower = Subtract(CreateConstant(constraint.Interval.LowerBound), (ISymbolicExpressionTree)treeForDerivation.Clone());
+            // convert variables named theta back to constants
+            var df_prepared = ReplaceVarWithConst(f_larger_lower, thetaNames, thetaValues, allThetaNodes);
+            constraintTrees.Add(df_prepared);
+          }
+        }
+      using (var state = new ConstrainedNLSInternal(solver, tree, maxIterations, problemData, 0, 0, 0)) {
+        state.Optimize();
+        return state.BestError;
+      }
+      var preparedTree = ReplaceVarWithConst(treeForDerivation, thetaNames, thetaValues, allThetaNodes);
+      var preparedTreeParameterNodes = GetParameterNodes(preparedTree, allThetaNodes);
+      // local function
+      void UpdateThetaValues(double[] theta) {
+        for (int i = 0; i < theta.Length; ++i) {
+          foreach (var constNode in allThetaNodes[i]) constNode.Value = theta[i];
+        }
+      }
+      var fi_eval = new double[target.Length];
+      var jac_eval = new double[target.Length, thetaValues.Count];
+      double calculate_obj(uint dim, double[] curX, double[] grad, IntPtr data) {
+        UpdateThetaValues(curX);
+        if (grad != null) {
+          var autoDiffEval = new VectorAutoDiffEvaluator();
+          autoDiffEval.Evaluate(preparedTree, problemData.Dataset, trainingRows,
+            preparedTreeParameterNodes, fi_eval, jac_eval);
+          // calc sum of squared errors and gradient
+          var sse = 0.0;
+          for (int j = 0; j < grad.Length; j++) grad[j] = 0;
+          for (int i = 0; i < target.Length; i++) {
+            var r = target[i] - fi_eval[i];
+            sse += 0.5 * r * r;
+            for (int j = 0; j < grad.Length; j++) {
+              grad[j] -= r * jac_eval[i, j];
+            }
+          }
+          if (double.IsNaN(sse)) return double.MaxValue;
+          // average
+          for (int j = 0; j < grad.Length; j++) { grad[j] /= target.Length; }
+          return sse / target.Length;
+        } else {
+          var eval = new VectorEvaluator();
+          var prediction = eval.Evaluate(preparedTree, problemData.Dataset, trainingRows);
+          // calc sum of squared errors and gradient
+          var sse = 0.0;
+          for (int i = 0; i < target.Length; i++) {
+            var r = target[i] - prediction[i];
+            sse += 0.5 * r * r;
+          }
+          if (double.IsNaN(sse)) return double.MaxValue;
+          // average
+          return sse / target.Length;
+        }
+      }
+      double calculate_constraint(uint dim, double[] curX, double[] grad, IntPtr data) {
+        UpdateThetaValues(curX);
+        var intervalEvaluator = new IntervalEvaluator();
+        var constraintData = Marshal.PtrToStructure<ConstraintData>(data);
+        if (grad != null) for (int j = 0; j < grad.Length; j++) grad[j] = 0; // clear grad
+        var interval = intervalEvaluator.Evaluate(constraintData.Tree, dataIntervals, constraintData.ParameterNodes,
+          out double[] lowerGradient, out double[] upperGradient);
+        // we transformed this to a constraint c(x) <= 0, so only the upper bound is relevant for us
+        if (grad != null) for (int j = 0; j < grad.Length; j++) { grad[j] = upperGradient[j]; }
+        if (double.IsNaN(interval.UpperBound)) return double.MaxValue;
+        else return interval.UpperBound;
+      }
+      var minVal = Math.Min(-1000.0, thetaValues.Min());
+      var maxVal = Math.Max(1000.0, thetaValues.Max());
+      var lb = Enumerable.Repeat(minVal, thetaValues.Count).ToArray();
+      var up = Enumerable.Repeat(maxVal, thetaValues.Count).ToArray();
+      IntPtr nlopt_opt = NLOpt.nlopt_create(GetAlgFromIdentifier(solver), (uint)thetaValues.Count); /* algorithm and dimensionality */
+      NLOpt.nlopt_set_lower_bounds(nlopt_opt, lb);
+      NLOpt.nlopt_set_upper_bounds(nlopt_opt, up);
+      var calculateObjectiveDelegate = new NLOpt.nlopt_func(calculate_obj); // keep a reference to the delegate (see below)
+      NLOpt.nlopt_set_min_objective(nlopt_opt, calculateObjectiveDelegate, IntPtr.Zero);
+      var constraintDataPtr = new IntPtr[constraintTrees.Count];
+      var calculateConstraintDelegates = new NLOpt.nlopt_func[constraintTrees.Count]; // make sure we keep a reference to the delegates (otherwise GC will free delegate objects see https://stackoverflow.com/questions/7302045/callback-delegates-being-collected#7302258)
+      for (int i = 0; i < constraintTrees.Count; i++) {
+        var constraintData = new ConstraintData() { Tree = constraintTrees[i], ParameterNodes = GetParameterNodes(constraintTrees[i], allThetaNodes) };
+        constraintDataPtr[i] = Marshal.AllocHGlobal(Marshal.SizeOf<ConstraintData>());
+        Marshal.StructureToPtr(constraintData, constraintDataPtr[i], fDeleteOld: false);
+        calculateConstraintDelegates[i] = new NLOpt.nlopt_func(calculate_constraint);
+        NLOpt.nlopt_add_inequality_constraint(nlopt_opt, calculateConstraintDelegates[i], constraintDataPtr[i], 1e-8);
+      }
+      NLOpt.nlopt_set_xtol_rel(nlopt_opt, 1e-4);
+      NLOpt.nlopt_set_maxtime(nlopt_opt, 10.0); // 10 secs
+      NLOpt.nlopt_set_maxeval(nlopt_opt, maxIterations);
+      var x = thetaValues.ToArray();  /* initial guess */
+      double minf = double.MaxValue; /* minimum objective value upon return */
+      var res = NLOpt.nlopt_optimize(nlopt_opt, x, ref minf);
+      if (res < 0) {
+        throw new InvalidOperationException($"NLOpt failed {res} {NLOpt.nlopt_get_errmsg(nlopt_opt)}");
+      } else {
+        // update parameters in tree
+        var pIdx = 0;
+        // here we lose the two last parameters (for linear scaling)
+        foreach (var node in tree.IterateNodesPostfix()) {
+          if (node is ConstantTreeNode constTreeNode) {
+            constTreeNode.Value = x[pIdx++];
+          } else if (node is VariableTreeNode varTreeNode) {
+            varTreeNode.Weight = x[pIdx++];
+          }
+        }
+        // note: we keep the optimized constants even when the tree is worse.
+        // assert that we lose the last two parameters
+        if (pIdx != x.Length - 2) throw new InvalidProgramException();
+      }
+      NLOpt.nlopt_destroy(nlopt_opt);
+      for (int i = 0; i < constraintDataPtr.Length; i++)
+        Marshal.FreeHGlobal(constraintDataPtr[i]);
+      counter.FunctionEvaluations += NLOpt.nlopt_get_numevals(nlopt_opt);
+      // counter.GradientEvaluations += NLOpt.nlopt_get; // TODO
+      return Math.Min(minf, targetVariance);
+    }
+    private static NLOpt.nlopt_algorithm GetAlgFromIdentifier(string solver) {
+      if (solver.Contains("MMA")) return NLOpt.nlopt_algorithm.NLOPT_LD_MMA;
+      if (solver.Contains("COBYLA")) return NLOpt.nlopt_algorithm.NLOPT_LN_COBYLA;
+      if (solver.Contains("CCSAQ")) return NLOpt.nlopt_algorithm.NLOPT_LD_CCSAQ;
+      if (solver.Contains("ISRES")) return NLOpt.nlopt_algorithm.NLOPT_GN_ISRES;
+      throw new ArgumentException($"Unknown solver {solver}");
+    }
+    private static ISymbolicExpressionTree CopyAndScaleTree(ISymbolicExpressionTree tree, double scalingFactor, double offset) {
+      var m = (ISymbolicExpressionTree)tree.Clone();
+      var add = MakeNode<Addition>(MakeNode<Multiplication>(m.Root.GetSubtree(0).GetSubtree(0), CreateConstant(scalingFactor)), CreateConstant(offset));
+      m.Root.GetSubtree(0).RemoveSubtree(0);
+      m.Root.GetSubtree(0).AddSubtree(add);
+      return m;
+    }
+    #region helper
+    private static ISymbolicExpressionTreeNode[] GetParameterNodes(ISymbolicExpressionTree tree, List<ConstantTreeNode>[] allNodes) {
+      // TODO better solution necessary
+      var treeConstNodes = tree.IterateNodesPostfix().OfType<ConstantTreeNode>().ToArray();
+      var paramNodes = new ISymbolicExpressionTreeNode[allNodes.Length];
+      for (int i = 0; i < paramNodes.Length; i++) {
+        paramNodes[i] = allNodes[i].SingleOrDefault(n => treeConstNodes.Contains(n));
+      }
+      return paramNodes;
+    }
+    private static ISymbolicExpressionTree ReplaceVarWithConst(ISymbolicExpressionTree tree, List<string> thetaNames, List<double> thetaValues, List<ConstantTreeNode>[] thetaNodes) {
+      var copy = (ISymbolicExpressionTree)tree.Clone();
+      var nodes = copy.IterateNodesPostfix().ToList();
+      for (int i = 0; i < nodes.Count; i++) {
+        var n = nodes[i] as VariableTreeNode;
+        if (n != null) {
+          var thetaIdx = thetaNames.IndexOf(n.VariableName);
+          if (thetaIdx >= 0) {
+            var parent = n.Parent;
+            if (thetaNodes[thetaIdx].Any()) {
+              // HACK: REUSE CONSTANT TREE NODE IN SEVERAL TREES
+              // we use this trick to allow autodiff over thetas when thetas occurr multiple times in the tree (e.g. in derived trees)
+              var constNode = thetaNodes[thetaIdx].First();
+              var childIdx = parent.IndexOfSubtree(n);
+              parent.RemoveSubtree(childIdx);
+              parent.InsertSubtree(childIdx, constNode);
+            } else {
+              var constNode = (ConstantTreeNode)CreateConstant(thetaValues[thetaIdx]);
+              var childIdx = parent.IndexOfSubtree(n);
+              parent.RemoveSubtree(childIdx);
+              parent.InsertSubtree(childIdx, constNode);
+              thetaNodes[thetaIdx].Add(constNode);
+            }
+          }
+        }
+      }
+      return copy;
+    }
+    private static ISymbolicExpressionTree ReplaceConstWithVar(ISymbolicExpressionTree tree, out List<string> thetaNames, out List<double> thetaValues) {
+      thetaNames = new List<string>();
+      thetaValues = new List<double>();
+      var copy = (ISymbolicExpressionTree)tree.Clone();
+      var nodes = copy.IterateNodesPostfix().ToList();
+      int n = 1;
+      for (int i = 0; i < nodes.Count; ++i) {
+        var node = nodes[i];
+        if (node is ConstantTreeNode constantTreeNode) {
+          var thetaVar = (VariableTreeNode)new Problems.DataAnalysis.Symbolic.Variable().CreateTreeNode();
+          thetaVar.Weight = 1;
+          thetaVar.VariableName = $"θ{n++}";
+          thetaNames.Add(thetaVar.VariableName);
+          thetaValues.Add(constantTreeNode.Value);
+          var parent = constantTreeNode.Parent;
+          if (parent != null) {
+            var index = constantTreeNode.Parent.IndexOfSubtree(constantTreeNode);
+            parent.RemoveSubtree(index);
+            parent.InsertSubtree(index, thetaVar);
+          }
+        }
+        if (node is VariableTreeNode varTreeNode) {
+          var thetaVar = (VariableTreeNode)new Problems.DataAnalysis.Symbolic.Variable().CreateTreeNode();
+          thetaVar.Weight = 1;
+          thetaVar.VariableName = $"θ{n++}";
+          thetaNames.Add(thetaVar.VariableName);
+          thetaValues.Add(varTreeNode.Weight);
+          var parent = varTreeNode.Parent;
+          if (parent != null) {
+            var index = varTreeNode.Parent.IndexOfSubtree(varTreeNode);
+            parent.RemoveSubtree(index);
+            var prodNode = MakeNode<Multiplication>();
+            varTreeNode.Weight = 1.0;
+            prodNode.AddSubtree(varTreeNode);
+            prodNode.AddSubtree(thetaVar);
+            parent.InsertSubtree(index, prodNode);
+          }
+        }
+      }
+      return copy;
+    }
+    private static ISymbolicExpressionTreeNode CreateConstant(double value) {
+      var constantNode = (ConstantTreeNode)new Constant().CreateTreeNode();
+      constantNode.Value = value;
+      return constantNode;
+    }
+    private static ISymbolicExpressionTree Subtract(ISymbolicExpressionTree t, ISymbolicExpressionTreeNode b) {
+      var sub = MakeNode<Subtraction>(t.Root.GetSubtree(0).GetSubtree(0), b);
+      t.Root.GetSubtree(0).RemoveSubtree(0);
+      t.Root.GetSubtree(0).InsertSubtree(0, sub);
+      return t;
+    }
+    private static ISymbolicExpressionTree Subtract(ISymbolicExpressionTreeNode b, ISymbolicExpressionTree t) {
+      var sub = MakeNode<Subtraction>(b, t.Root.GetSubtree(0).GetSubtree(0));
+      t.Root.GetSubtree(0).RemoveSubtree(0);
+      t.Root.GetSubtree(0).InsertSubtree(0, sub);
+      return t;
+    }
+    private static ISymbolicExpressionTreeNode MakeNode<T>(params ISymbolicExpressionTreeNode[] fs) where T : ISymbol, new() {
+      var node = new T().CreateTreeNode();
+      foreach (var f in fs) node.AddSubtree(f);
+      return node;
+    }
+    #endregion
+    private static void UpdateConstants(ISymbolicExpressionTreeNode[] nodes, double[] constants) {
+      if (nodes.Length != constants.Length) throw new InvalidOperationException();
+      for (int i = 0; i < nodes.Length; i++) {
+        if (nodes[i] is VariableTreeNode varNode) varNode.Weight = constants[i];
+        else if (nodes[i] is ConstantTreeNode constNode) constNode.Value = constants[i];
+      }
+    }
+    private static alglib.ndimensional_fvec CreateFunc(ISymbolicExpressionTree tree, VectorEvaluator eval, ISymbolicExpressionTreeNode[] parameterNodes, IDataset ds, string targetVar, int[] rows) {
+      var y = ds.GetDoubleValues(targetVar, rows).ToArray();
+      return (double[] c, double[] fi, object o) => {
+        UpdateConstants(parameterNodes, c);
+        var pred = eval.Evaluate(tree, ds, rows);
+        for (int i = 0; i < fi.Length; i++)
+          fi[i] = pred[i] - y[i];
+        var counter = (EvaluationsCounter)o;
+        counter.FunctionEvaluations++;
+      };
+    }
+    private static alglib.ndimensional_jac CreateJac(ISymbolicExpressionTree tree, VectorAutoDiffEvaluator eval, ISymbolicExpressionTreeNode[] parameterNodes, IDataset ds, string targetVar, int[] rows) {
+      var y = ds.GetDoubleValues(targetVar, rows).ToArray();
+      return (double[] c, double[] fi, double[,] jac, object o) => {
+        UpdateConstants(parameterNodes, c);
+        eval.Evaluate(tree, ds, rows, parameterNodes, fi, jac);
+        for (int i = 0; i < fi.Length; i++)
+          fi[i] -= y[i];
+        var counter = (EvaluationsCounter)o;
+        counter.GradientEvaluations++;
+      };
+    }
+    public static bool CanOptimizeConstants(ISymbolicExpressionTree tree) {
+      return TreeToAutoDiffTermConverter.IsCompatible(tree);
+    }
+    }
+  }
+}

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Changeset 17215 for branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Regression.Symbolic.Extensions

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branches/2994-AutoDiffForIntervals/HeuristicLab.Problems.DataAnalysis.Regression.Symbolic.Extensions/NLOptEvaluator.cs

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