randomized rounding for spsa

spsa converts floating point parameter values to integers via round(),
which is dicontinuous.  This patch adds randomized rounding,
which converts x+p (where x is integer and p is within [0,1)) to
x with probability 1-p and x+1 with probability p (thus we get back x+p
in expectation), which is continuous.

fishtest/fishtest/rundb.py

@@ -1,6 +1,7 @@
 import copy
 import os
 import random
+import math
 import time
 from datetime import datetime
 from bson.objectid import ObjectId
@@ -355,13 +356,27 @@ def approve_run(self, run_id, approver):
     self.runs.save(run)
     return True
 
-  def spsa_param_clip(param, increment, clipping):
+  def spsa_param_clip_round(param, increment, clipping, rounding):
+    value = 0.0
+
     if clipping == 'old':
-      return min(max(param['theta'] + increment, param['min']), param['max'])
+      value = min(max(param['theta'] + increment, param['min']), param['max'])
     else: #clipping == 'careful':
       inc = min(abs(increment), abs(param['theta'] - param['min']) / 2, abs(param['theta'] - param['max']) / 2)
       inc_sgn = 0 if increment == 0 else increment / abs(increment)
-      return param['theta'] + inc_sgn * inc
+      value = param['theta'] + inc_sgn * inc
+
+    #'deterministic' rounding calls round() inside the worker.
+    #'randomized' says 4.p should be 5 with probability p, 4 with probability 1-p,
+    #  and is continuous (albeit after expectation) unlike round().
+    if rounding == 'randomized':
+        fl = math.floor(value) #greatest integer <= value, thus works for negative.
+        if random.uniform(0,1) < value - fl:
+            value = fl + 1
+        else:
+            value = fl
+
+    return value
 
   def request_spsa(self, run_id, task_id):
     run = self.get_run(run_id)
@@ -381,6 +396,8 @@ def request_spsa(self, run_id, task_id):
     spsa = run['args']['spsa']
     if 'clipping' not in spsa:
         spsa['clipping'] = 'old'
+    if 'rounding' not in spsa:
+        spsa['rounding'] = 'deterministic'
 
     # Generate the next set of tuning parameters
     iter_local = spsa['iter'] + 1 #assume at least one completed, and avoid division by zero
@@ -391,14 +408,14 @@ def request_spsa(self, run_id, task_id):
       flip = 1 if bool(random.getrandbits(1)) else -1
       result['w_params'].append({
         'name': param['name'],
-        'value': spsa_param_clip(param, c * flip, spsa['clipping']),
+        'value': spsa_param_clip_round(param, c * flip, spsa['clipping'], spsa['rounding']),
         'R': R,
         'c': c,
         'flip': flip,
       })
       result['b_params'].append({
         'name': param['name'],
-        'value': spsa_param_clip(param, -c * flip, spsa['clipping']),
+        'value': spsa_param_clip_round(param, -c * flip, spsa['clipping'], spsa['rounding']),
       })
 
     return result
@@ -418,7 +435,7 @@ def update_spsa(self, run, spsa_results):
       R = spsa_results['w_params'][idx]['R']
       c = spsa_results['w_params'][idx]['c']
       flip = spsa_results['w_params'][idx]['flip']
-      param['theta'] = spsa_param_clip(param, R * c * result * flip, spsa['clipping']),
+      param['theta'] = spsa_param_clip_round(param, R * c * result * flip, spsa['clipping'], 'deterministic'),
       summary.append({
         'theta': param['theta'],
         'R': R,

fishtest/fishtest/templates/tests_run.mak

@@ -119,6 +119,15 @@ Cowardice,150,0,200,10,0.0020"""})['raw_params']}</textarea>
       </select>
     </div>
   </div>
+  <div class="control-group stop_rule spsa">
+    <label class="control-label">SPSA rounding:</label>
+    <div class="controls">
+      <select name="spsa_rounding">
+        <option value="deterministic">deterministic</option>
+        <option value="randomized">randomized</option>
+      </select>
+    </div>
+  </div>
   <div class="control-group">
     <label class="control-label">Time Control:</label>
     <div class="controls">

fishtest/fishtest/views.py

@@ -302,6 +302,7 @@ def validate_form(request):
       'iter': 0,
       'num_iter': int(data['num_games'] / 2),
       'clipping': request.POST['spsa_clipping'],
+      'rounding': request.POST['spsa_rounding'],
     }
     data['spsa']['params'] = parse_spsa_params(request.POST['spsa_raw_params'], data['spsa'])
   else:
@@ -679,8 +680,10 @@ def tests_view(request):
     if name == 'spsa' and value != '-':
       params = ['param: %s, best: %.2f, start: %.2f, min: %.2f, max: %.2f, c %f, a %f' % \
                 (p['name'], p['theta'], p['start'], p['min'], p['max'], p['c'], p['a']) for p in value['params']]
-      value = 'Iter: %d, A: %d, alpha %f, gamma %f, clipping %s\n%s' % (value['iter'], value['A'], value['alpha'], \
-                value['gamma'], value['clipping'] if 'clipping' in value else 'old', '\n'.join(params))
+      value = 'Iter: %d, A: %d, alpha %f, gamma %f, clipping %s, rounding %s\n%s' % (value['iter'], value['A'], value['alpha'], value['gamma'],
+              value['clipping'] if 'clipping' in value else 'old',
+              value['rounding'] if 'rounding' in value else 'deterministic',
+              '\n'.join(params))
 
     if 'tests_repo' in run['args']:
       if name == 'new_tag':