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"# Building MDPs\n",
"A Markov Decision Process is an extended Markov Chain which\n",
"\n",
"* states\n",
"* actions\n",
"* transitions\n",
"\n",
"Where\n",
"\n",
"* actions are essentially 'decisions' which might be decided by *schedulers*/*policies*/*agents* (these terms are equivalent)\n",
"* each state has a number of actions\n",
"* actions have probabilistic transitions to states\n",
"\n",
"In general, for smaller models, the model API is more convenient, but for bigger models the pgc API becomes more convenient.\n",
"\n",
"Here we show how to construct a simple example mdp using the pgc API and the model builder API. \n",
"The idea is that you can choose to study (you will likely pass the exam but you have less free time) or not to study (you will have more free time but risk failing the exam)."
]
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"Test request failed. See 'Communication server remark' in docs. Disable warning by use_server=False.\n"
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"source": [
"from stormvogel import pgc\n",
"from stormvogel.model import EmptyAction, ModelType\n",
"from stormvogel.show import show\n",
"from stormvogel.layout import Layout\n",
"\n",
"init = pgc.State(x=\"\")\n",
"\n",
"def available_actions(s: pgc.State):\n",
" if s == init: # If we are in the initial state, we have a choice.\n",
" return [pgc.Action([\"study\"]), pgc.Action([\"don't study\"])]\n",
" else: # Otherwise, we don't have any choice, we are just a Markov chain. \n",
" return [pgc.Action([])]\n",
"\n",
"def delta(s: pgc.State, a: pgc.Action):\n",
" if \"study\" in a.labels:\n",
" return [(1, pgc.State(x=[\"studied\"]))]\n",
" elif \"don't study\" in a.labels:\n",
" return [(1, pgc.State(x=[\"didn't study\"]))]\n",
" elif \"studied\" in s.x:\n",
" return [(9/10, pgc.State(x=[\"pass test\"])), (1/10, pgc.State(x=[\"fail test\"]))]\n",
" elif \"didn't study\" in s.x:\n",
" return [(2/5, pgc.State(x=[\"pass test\"])), (3/5, pgc.State(x=[\"fail test\"]))]\n",
" else:\n",
" return [(1, pgc.State(x=[\"end\"]))]\n",
"\n",
"labels = lambda s: s.x\n",
"\n",
"# For rewards, you have to provide a list. This enables multiple reward models if you use a non-singleton list.\n",
"def rewards(s: pgc.State, a: pgc.Action):\n",
" if \"pass test\" in s.x:\n",
" return {\"r1\":100}\n",
" if \"didn't study\" in s.x:\n",
" return {\"r1\":15}\n",
" else:\n",
" return {\"r1\":0}\n",
"\n",
"\n",
"pgc_study = pgc.build_pgc(\n",
" delta=delta,\n",
" initial_state_pgc=init,\n",
" available_actions=available_actions,\n",
" labels=labels,\n",
" modeltype=ModelType.MDP,\n",
" rewards=rewards\n",
")\n",
"vis = show(pgc_study, layout=Layout(\"layouts/pinkgreen.json\"))"
]
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"source": [
"import stormvogel.model\n",
"from stormvogel.layout import Layout\n",
"from stormvogel.show import show\n",
"from stormvogel.model import EmptyAction\n",
"\n",
"mdp = stormvogel.model.new_mdp(\"Study\")\n",
"\n",
"init = mdp.get_initial_state()\n",
"study = mdp.action(\"study\")\n",
"not_study = mdp.action(\"don't study\")\n",
"\n",
"studied = mdp.new_state(\"studied\")\n",
"not_studied = mdp.new_state(\"didn't study\")\n",
"pass_test = mdp.new_state(\"pass test\")\n",
"fail_test = mdp.new_state(\"fail test\")\n",
"end = mdp.new_state(\"end\")\n",
"\n",
"init.set_transitions([\n",
" (study, studied),\n",
" (not_study, not_studied)\n",
"])\n",
"\n",
"studied.set_transitions([\n",
" (9/10, pass_test),\n",
" (1/10, fail_test)\n",
"])\n",
"\n",
"not_studied.set_transitions([\n",
" (4/10, pass_test),\n",
" (6/10, fail_test)\n",
"])\n",
"\n",
"pass_test.set_transitions([(1, end)])\n",
"fail_test.set_transitions([(1, end)])\n",
"\n",
"reward_model = mdp.add_rewards(\"R\")\n",
"reward_model.set_state_action_reward(pass_test, EmptyAction, 100)\n",
"reward_model.set_state_action_reward(fail_test, EmptyAction, 0)\n",
"reward_model.set_state_action_reward(not_studied, EmptyAction, 15)\n",
"reward_model.set_unset_rewards(0)\n",
"\n",
"vis = show(mdp, layout=Layout(\"layouts/pinkgreen.json\"), name=\"study\")"
]
},
{
"cell_type": "markdown",
"id": "664af5c9-cecc-4890-8b7d-5e24404451bb",
"metadata": {},
"source": [
"A famous but more involved example of an MDP is the Monty Hall problem. We will show how to construct it using the pgc API."
]
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"source": [
"from stormvogel import pgc\n",
"from stormvogel.model import EmptyAction, ModelType\n",
"from stormvogel.show import show\n",
"from stormvogel.layout import Layout\n",
"\n",
"init = pgc.State(x=\"\")\n",
"\n",
"empty_action = pgc.Action([])\n",
"\n",
"def available_actions(s: pgc.State):\n",
" if \"carchosen\" in s.x:\n",
" return [pgc.Action([\"open\", str(i)]) for i in range(1,4)]\n",
" elif \"opened\" in s.x:\n",
" return [pgc.Action([\"stay\"]), pgc.Action([\"switch\"])]\n",
" return [empty_action]\n",
" \n",
"\n",
"def delta(s: pgc.State, a: pgc.Action):\n",
" if s == init:\n",
" return [(1/3, pgc.State(x=[\"carchosen\", str(i)], car=i)) for i in range(1,4)]\n",
" elif \"open\" in a.labels:\n",
" return [(1, pgc.State(x=[\"open\", str(a.labels[1])], car=s.car, chosen=a.labels[1]))]\n",
" elif \"open\" in s.x:\n",
" possible_goats = set([1,2,3]) - {s.car} - {s.chosen}\n",
" return [(1/len(possible_goats), \n",
" pgc.State(x=[\"opened\", str(s.chosen), f\"goat,{i}\"], \n",
" car=s.car, goat=i, chosen=s.chosen)) \n",
" for i in possible_goats]\n",
" elif \"stay\" in a.labels:\n",
" return [(1, pgc.State(x=[\"won\"], pred=s))] if s.chosen == s.car else [(1, pgc.State(x=[\"lost\"], pred=s))]\n",
" elif \"switch\" in a.labels:\n",
" return [(1, pgc.State(x=[\"won\"], pred=s))] if s.chosen != s.car else [(1, pgc.State(x=[\"lost\"], pred=s))]\n",
" else:\n",
" return [(1, s)]\n",
" \n",
"labels = lambda s: s.x\n",
"\n",
"pgc_die = pgc.build_pgc(\n",
" delta=delta,\n",
" initial_state_pgc=init,\n",
" available_actions=available_actions,\n",
" labels=labels,\n",
" modeltype=ModelType.MDP\n",
")\n",
"\n",
"vis2 = show(pgc_die, layout=Layout(\"layouts/monty.json\"))"
]
},
{
"cell_type": "markdown",
"id": "df6ed293-7203-409a-b68c-573818dfda74",
"metadata": {},
"source": [
"And here is a way to do it using the model API. Do note that this model is slightly different!"
]
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"source": [
"# We create the monty hall mdp\n",
"mdp = stormvogel.model.new_mdp(\"Monty Hall\")\n",
"\n",
"init = mdp.get_initial_state()\n",
"\n",
"# first choose car position\n",
"init.set_transitions(\n",
" [(1 / 3, mdp.new_state(\"carchosen\", {\"car_pos\": i})) for i in range(3)]\n",
")\n",
"\n",
"# we choose a door in each case\n",
"for s in mdp.get_states_with_label(\"carchosen\"):\n",
" s.set_transitions(\n",
" [\n",
" (\n",
" mdp.action(f\"open{i}\"),\n",
" mdp.new_state(\"open\", s.valuations | {\"chosen_pos\": i}),\n",
" )\n",
" for i in range(3)\n",
" ]\n",
" )\n",
"\n",
"# the other goat is revealed\n",
"for s in mdp.get_states_with_label(\"open\"):\n",
" car_pos = s.valuations[\"car_pos\"]\n",
" chosen_pos = s.valuations[\"chosen_pos\"]\n",
" other_pos = {0, 1, 2} - {car_pos, chosen_pos}\n",
" s.set_transitions(\n",
" [\n",
" (\n",
" 1 / len(other_pos),\n",
" mdp.new_state(\"goatrevealed\", s.valuations | {\"reveal_pos\": i}),\n",
" )\n",
" for i in other_pos\n",
" ]\n",
" )\n",
"\n",
"# we must choose whether we want to switch\n",
"for s in mdp.get_states_with_label(\"goatrevealed\"):\n",
" car_pos = s.valuations[\"car_pos\"]\n",
" chosen_pos = s.valuations[\"chosen_pos\"]\n",
" reveal_pos = s.valuations[\"reveal_pos\"]\n",
" other_pos = list({0, 1, 2} - {reveal_pos, chosen_pos})[0]\n",
" s.set_transitions(\n",
" [\n",
" (\n",
" mdp.action(\"stay\"),\n",
" mdp.new_state(\n",
" [\"done\"] + ([\"target\"] if chosen_pos == car_pos else []),\n",
" s.valuations | {\"chosen_pos\": chosen_pos},\n",
" ),\n",
" ),\n",
" (\n",
" mdp.action(\"switch\"),\n",
" mdp.new_state(\n",
" [\"done\"] + ([\"target\"] if other_pos == car_pos else []),\n",
" s.valuations | {\"chosen_pos\": other_pos},\n",
" ),\n",
" ),\n",
" ]\n",
" )\n",
"\n",
"# we add self loops to all states with no outgoing transitions\n",
"mdp.add_self_loops()\n",
"vis = show(mdp, layout=Layout(\"layouts/monty.json\"))"
]
},
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