# for training policy
    def train_one_epoch():
        # make some empty lists for logging.
        batch_obs = []          # for observations
        batch_acts = []         # for actions
        batch_weights = []      # for R(tau) weighting in policy gradient
        batch_rets = []         # for measuring episode returns
        batch_lens = []         # for measuring episode lengths

        # reset episode-specific variables
        obs = env.reset()       # first obs comes from starting distribution
        done = False            # signal from environment that episode is over
        ep_rews = []            # list for rewards accrued throughout ep

        # render first episode of each epoch
        finished_rendering_this_epoch = False

        # collect experience by acting in the environment with current policy
        while True:

            # rendering
            if not(finished_rendering_this_epoch):
                env.render()

            # save obs
            batch_obs.append(obs.copy())

            # act in the environment
            act = sess.run(actions, {obs_ph: obs.reshape(1,-1)})[0]
            obs, rew, done, _ = env.step(act)

            # save action, reward
            batch_acts.append(act)
            ep_rews.append(rew)

            if done:
                # if episode is over, record info about episode
                ep_ret, ep_len = sum(ep_rews), len(ep_rews)
                batch_rets.append(ep_ret)
                batch_lens.append(ep_len)

                # the weight for each logprob(a|s) is R(tau)
                batch_weights += [ep_ret] * ep_len

                # reset episode-specific variables
                obs, done, ep_rews = env.reset(), False, []

                # won't render again this epoch
                finished_rendering_this_epoch = True

                # end experience loop if we have enough of it
                if len(batch_obs) > batch_size:
                    break

        # take a single policy gradient update step
        batch_loss, _ = sess.run([loss, train_op],
                                 feed_dict={
                                    obs_ph: np.array(batch_obs),
                                    act_ph: np.array(batch_acts),
                                    weights_ph: np.array(batch_weights)
                                 })
        return batch_loss, batch_rets, batch_lens